I’ve had a similar experience with Mormons, and have chatted a bit with an ex-Mormon Christian, so here are my reflections on it.
Yes, they are wrong and there’s plenty of places in the Bible that contradict their teaching, but pointing to them won’t necessarily convince a Mormon. They assert that new revelation was given to Joseph Smith in the 1800’s, so a “newer is better” argument works for them, even if it’s flawed. They’ll just say that God corrected himself the next time. As you look into the details of this ‘revelation’ it’s all a bit fantastic, with magic spectacles and mysterious golden plates.
Salvation, for a Mormon, is by works, which is why they’re so keen to come back to you. Any part of the Bible that speaks of salvation by grace through faith would be good to have in mind. (e.g. 2tim 3:15, Eph 2:8-9, Heb 11). If they’re missionaries from Utah, say, then they are solidly indoctrinated to believe that any criticism you make is an attack of Satan himself. As you open your mouth, the shutters go up and it’s all over. You can’t really convince them of truths from the Bible, which is really frustrating!
What hope is there then? Lots!
You can actually give them a reason to turn to Jesus: Assurance. Those with faith in Christ WILL be saved aside from works. We have confidence in the hope we share in Christ. It leads to Joy and Love, which is something they don’t have. Pray, and show some love for them, and see what God does… Even giving a cool glass of water would be a shock to them, since they get so many doors slammed in their faces.
(Just a note of caution: Mormons aren’t idiots. There’s something attractive to their lies, so don’t get sucked in!)
PS: The book “So What’s the Difference” is a bit dated now, but is still really helpful.