How do you fix/remove rear window surround trim?

The specialty tool certainly helps, but, you can make one or use a couple of screw drivers if you're real careful. It's a matter of triggering the clip to release the molding. It sort of fish-hooks the edge of the molding. Your lower molding looks like it will need replacing, so, I'd start with trying to remove that first. Use a putty knife or similar to slightly pry the inner edge of the molding on the bent end away from the glass/gasket. Then slide whatever tool you choose along the groove on the outer edge of the molding to locate the clip. Then the tricky part is trying to convince the clip to let go of the molding. Once you have done a couple, you'll get a better idea of how they're fastened. I agree that you will probably have to pull all the moldings, the glass, and the gasket to replace the clips and reinstall everything. If the gasket is still fairly pliable, that can be saved and reused if need be. Check for availability on that first before you tackle it. I'd have the new gasket in hand before deciding to cut the old one.