How do you fix/remove rear window surround trim?

The right tools and a bit of knowledge is all it takes.
Whatever you do DO NOT use silicone to seal the window with. You can use a tube of roof caulking and it'll work just fine
Agreed. Silicone is not an auto body repair material. Just to be a little clearer on the "roof caulking" maybe it should be a little more specific as to what kind of roof caulking we are talking about here. I used some awesome stuff called "Through The Roof" for temporary repairs when a 75 ft. Ponderosa Pine decided to (with some wind help) occupy some space in my living room. The sealer is clear and smells like good old model airplane glue. Not that there is anything wrong with that. :) Anyway, as good as I think the Through The Roof product would work sealing up a leak on just about anything, I sure would hate to have to get back into it on an auto repair, much like silicone.
I suppose we could assume it is the "asphalt" based roof caulking you were referring to. I have never used it on a car myself but not a bad idea either.