According to your explanation, Gil wants to getting back with Lars, which shows that Gil still has feelings for Lars. But this can't explain Gil's behavior of touching Parker, Since you are still thinking about Lars, you should not do these things to Parker. This is disrespect to Parker. You can't do whatever you want just because Parker has a good temper.
I don't understand why you complain about the way Parker treats Gil. Obviously, the way Gil treats Parker is problematic. Parker is the one who should complain. You don't like Parker. Why did you touch him?