How to Answer a Mormon (this argument also works for legalistic versions of Christianity, other cults, and Jehovah's Witnesses). It is up to you whether you invite these young men into your home. It provides them with some sense of being welcomed, but it is also your home field. In general, it is a better place to have a decent discussion at the kitchen table than at the front door.
When you are approached at the door, the Mormon missionary will often start with some attempt to gain consent or agreement to principles of family life, being good, or Christian values. A better response is to use the Socratic Method and ask questions. Here is a method of approach that can work.
"Thank you for your concern for my welfare. May I ask you a question? Can anything be added to Christ's righteousness? Can He be made more righteous by anything that you or I do?"
Their response should be something along these lines. "No, God is perfect and perfectly righteous. So is His Son. You cannot add anything to make God more righteous or perfect."
"Okay, I agree with you on that. So, let me ask you another question. If your father or mother gave you $1,000 as a gift, a wedding present, or for your birthday, for example, do you have to do anything else to earn that gift? Isn't it yours, free and clear?"
"Their response should be something along the lines as, "I suppose not. It would be mine."
"That's what I think too. The Bible says that we have been given God's righteousness as a free gift. Since I have been given God's own righteousness, how could I be any more righteous than I already am? Could I become more righteous than God? Is there anything I could possibly add to God's gift of righteousness to make it more righteous? And since it is a free gift, what more could I do to receive something that has already been given to me? If I have to work for it, it is not a gift, is it?
"It says in Romans, that since we have all fallen short of the glory of God, we are made righteous by His grace as a gift, and that we have been given the free gift of righteousness through faith in Jesus Christ. Now are you trying to tell me that Jesus' righteousness is not enough, and that I need to believe something else to be righteous and be pleasing to God? Isn't what Jesus did for me on the Cross enough? Are you saying his sacrifice wasn't good enough? If I receive His righteousness by believing in Him, what else would I need to do?
"Let me ask you another question. If being righteous before God means that God is pleased with me, because God sees His righteousness in me, what else do I need to do to be pleasing to God?? I've been made righteous by God himself with His own righteousness! What could be better than that?"
Now from this point on, the discussion could go anywhere, with the missionaries falling back into some rote presentations that don't directly address the questions you've raised. If you can, hold their feet to the fire. Their arguments will always require Christ, faith, AND something else you need to do. That something else undermines the free gift of God's righteousness to you. It implies what God gave you isn't good enough to please God. A possible response to their doctrine that that you must do something else is: "God's own righteousness, which dwells in me, is powerful enough to conform me to His image over time, and He is surely able to bring the image of Jesus to bear on my nature. For it says in Romans that 'those whom He (God) foreknew He also predestined to be conformed to the image of His Son, and that those whom He predestined He also called; and those whom He called He also made righteous...' You see, it is God's business to complete in me what He has begun. It isn't something I can do on my own. He calls me, He makes me righteous by a gift of His own nature, and He has already decided that I will be conformed to the image of His Son Jesus."
Now, if the missionaries try to divert from this point, they will talk about how it is necessary to be baptized by a Mormon or some other such stuff: that faith in Jesus Christ is not sufficient, you have to do good works too. Here's the major problem with that shift in focus: the good news of what Jesus Christ has done for us is no longer good news. What Jesus did is not enough for us. His righteousness isn't good enough or sufficient. God gave us a defective type of righteousness. "Will any good works I do make me more righteous than God? If God gave me His perfect righteousness, how can I add to it? If it was a gift, I cannot earn it, and if it was perfect, I cannot complete it. It isn't what I do for God that counts, it is what God has done for me that is the Great News of the Gospel. If you are saying that I should be conformed to His image through cooperation with the Holy Spirit, I agree. But that is part of God's work in conforming me to the image of His Son. I cannot become more righteous than the perfect gift of God's own righteousness that was given to me in Jesus Christ!'
At this point, if they still want to assert that something else is necessary aside from faith in Christ, my response is to remind them that they must be under a curse. Because it says if anyone preaches a different gospel or good news other than the one Paul preached, he will be accursed: "But even if we, or an angel from heaven, should preach to you a great news contrary to that which we preached to you, let him be accursed. As we have said before, so now I say again, If any one is preaching to you a great news contrary to that which you received, let him be accursed," (Gal. 1:6 -9). So, the Mormons follow an angel that has preached a different gospel which is denying the grace of God in Jesus Christ. So they must have put themselves under a curse.
Let that sink in and see if you can help them.
These following scriptures are translations based upon the RSV. I have substituted the words for justification with the words made righteous, for in Greek the words are identical. Righteousness = justification. It could also be translated as declared innocent or found not guilty. It helps to translate it as righteousness for the modern ear because we tend not to understand or think in terms of legal justification. Justification tends to be impersonal, whereas God is a personal God, and He is not just concerned with legalities, but moral nature. So righteousness as a gift is a transformation of our intrinsic nature through the impartation of the Holy Spirit into our lives with rebirth. We are, as Paul says, new creations, made after the image and likeness of God. So if anyone is in Christ, he is a new creation:
Everything old has passed away; see, everything has become new! (2 Cor. 5:17).
But you are not in the flesh; you are in the Spirit, since the Spirit of God dwells in you. Anyone who does not have the Spirit of Christ does not belong to him, (Rom. 8:9).
You were taught to put away your former way of life, your old self, corrupt and deluded by its lusts, and to be renewed in the spirit of your minds, and to clothe yourselves with the new self, created according to the likeness of God in true righteousness and holiness, (Eph. 4:22 -24).)
I also translated the word Gospel, as Great News, since that is what it sounded like to its hearers: it is too good to be true. The technically accurate translation would be "good news" for that is what it means in Greek. But the words, good news, have become stale and have lost their impact. Great News is the better translation retaining the required impact for our day.
Scriptures on the Free Gift of God's Righteousness given to us.
For no human being will be made righteous in his sight by works of the law, since through the law comes knowledge of sin. But now the righteousness of God has been manifested apart from law, although the law and the prophets bear witness to it, the righteousness of God through faith in Jesus Christ for all who believe. For there is no distinction; since all have sinned and fall short of the glory of God, they are made righteous by his grace as a gift, through the redemption which is in Christ Jesus, whom God put forward as an expiation by his blood, to be received by faith. This was to show Gods righteousness, because in his divine forbearance he had passed over former sins; it was to prove at the present time that he himself is righteous and that he makes righteous him who has faith in Jesus. Then what becomes of our boasting? It is excluded. On what principle? On the principle of works? No, but on the principle of faith. For we hold that a man is made righteous by faith apart from works of law, (Rom. 3:20 -28).
But the free gift is not like the trespass. For if the many died through the one mans trespass, much more surely have the grace of God and the free gift in the grace of the one man, Jesus Christ, abounded for the many. And the free gift is not like the effect of the one mans sin. For the judgment following one trespass brought condemnation, but the free gift following many trespasses brings righteousness. If, because of the one mans trespass, death exercised dominion through that one, much more surely will those who receive the abundance of grace and the free gift of righteousness exercise dominion in life through the one man, Jesus Christ. Therefore just as one mans trespass led to condemnation for all, so one mans act of righteousness leads to righteousness and life for all. For just as by the one mans disobedience the many were made sinners, so by the one mans obedience the many will be made righteous, (Rom. 5:15 -19).
Scriptures that Point out Our Perfection is God's work in us, not ours:
For those whom he foreknew he also predestined to be conformed to the image of his Son, in order that he might be the first-born among many brethren. And those whom he predestined he also called; and those whom he called he also justified; and those whom he justified he also glorified. (Rom. 8:29 -30).
Scriptures that show how our attempts to perfect ourselves or make ourselves righteous apart from God's free gift cause us to turn away from Christ to a false teaching or counterfeit good news:
You are severed from Christ, you who would be made righteous by the law; you have fallen away from grace, (Gal. 5:4).
I am astonished that you are so quickly deserting him who called you in the grace of Christ and turning to a different great news-- not that there is another great news, but there are some who trouble you and want to pervert the great news of Christ. But even if we, or an angel from heaven, should preach to you a great news contrary to that which we preached to you, let him be accursed. As we have said before, so now I say again, If any one is preaching to you a great news contrary to that which you received, let him be accursed, (Gal. 1:6 -9).
We ourselves, who are Jews by birth and not Gentile sinners, yet who know that a man is not made righteous by works of the law but through faith in Jesus Christ, even we have believed in Christ Jesus, in order to be made righteous by faith in Christ, and not by works of the law, because by works of the law shall no one be made righteous, (Gal. 2:15 -16). For all who rely on works of the law are under a curse; for it is written, Cursed be every one who does not abide by all things written in the book of the law, and do them. Now it is evident that no man is made righteous before God by the law; for He who through faith is righteous shall live; but the law does not rest on faith, for He who does them shall live by them. Christ redeemed us from the curse of the law, having become a curse for us--for it is written, Cursed be every one who hangs on a tree-- that in Christ Jesus the blessing of Abraham might come upon the Gentiles, that we might receive the promise of the Spirit through faith, (Gal. 3:10 -14).