sort of thing.
Not quite on the same weird level, but the other day the missionaries came to our house during mid-day. My wife happened to be home. She was sick. They told her that they were on their way to an appointment and they wanted her to pray for them. Right there. On the front porch. She did it, but was horribly annoyed. (And we live in non-mo country).
These guys are young and dumb, and sort of delusional, and so I don't fault them. But there's a part of me that thinks they need to learn. Like, in your case, I think if I were you I'd call the mission pres, or at least the ward mission leader, to get the message to these guys that that's totally inappropriate.