Gil deserves Parker's lectures, but for Parker to call him Gilbert is hypocritical. As far as Parker is concerned it's fine when Parker does things, but Gil isn't allowed to do the exact same things. Does a character who would treat a close friend so unfairly deserve respect?
We agree on it being none of Parker's business. That's part of my issue with him.
Parker complains about his weight in several routes and wants to lose weight, but he doesn't want to put the work in by dieting. It wouldn't make sense for Gil to make up the whole thing about it being an exchange, it's too weird to make up.
In Mark's episode, Mark overhears Gil and Parker talking about how Parker needs to start watching his weight, which sounded to me like their agreement hadn't been made yet. Parker said Gil touches him rarely, so it's conceivable that Gil hasn't touched Parker after the agreement. And this also puts into question the issue of Gil being a virgin because of Parker and all the hypothetical people Parker might've cockblocked him from since that would've also been before their agreement. For a long time I disliked Gil because of his behavior, but I eventually realized Walter hadn't properly expressed that he didn't like it. If you do have Walter say so, Gil stops immediately. The way Parker lectures Gil focuses on how Gil shouldn't act this way to/in front of students. Similarly to Walter initially kinda disliking it but never really saying so, I assume Parker never really complained properly to Gil about touching him or Gil would've stopped already.
Lars knows about the agreement in Anders route and thinks it's unnecessary (though ironically Lars would bonk Gil for being lewd later).
The scene where Parker brags about all the people Gil could've slept with without him and Gil says he's a virgin because of Parker suggests otherwise.
I'm not saying Gil shouldn't be lectured for his behavior, but that it's hypocritical for Parker to call him Gilbert. Immature behavior or not, it's unfair. And he even does it when Gil hasn't done anything at the time to deserve it, or he thinks Gil isn't around.