Thinking about it again, I'm probably wrong about the divorce papers. I could've sworn I remember during Parker's story that Gil and Parker were together at one point, saying something along the lines of because they were together, Parker would watch Gil's inappropriate actions and Gil would watch over Parker's diet. I'm going to redo Parker's story and report back.
Edit: I skimmed through it and I was wrong about the papers and them being together. whoopsie
With you saying that Gil only mentioned that he dated Lars, that could just be because the three were together at the time. He didn't need to mention Parker.
Do I think Gil should stop teasing Parker? Yes. But why would Gil continue to tease Lars if they have broken up? On the other hand, even if Parker and Gil never had a relationship together, with Gil's inappropriate nature he would sure tease everyone. I also find it weird how when Walter said to stop Gil stops but with Parker he doesn't so yea.