Did Parker stop Lars and Gil? It seems that he just blushed after hearing Mark's description.
Why should Parker need Gil's help? Lars and Gil's plan is canceled. What's Parker's business?
I don't think Parker has any problem with the way he treats Gil. As you said, he just acts according to the agreement. On the contrary, Gil's behavior of touching Parker is problematic. When Parker doesn't like this behavior, Gil still does it, which is a little disrespectful to Parker. Don't forget that Gil asked Parker to stop his bad behavior, but he did these bad behaviors to Parker. This is ridiculous.
I'm not your lover, why should I allow you to touch me? Since you still have feelings for Lars, why don't you touch Lars?