The green screen is only part of the approach; it alone won’t give you the perspective warps, only a clean place to put the replacement video, which may look weird if the apparent angles don’t match up. And spill or reflection on the set from the green onto surrounding objects can make the comp more difficult.
My preferred approach would be to not put green on the screen at all, but either a flickering blue-white, or nothing at all, just the black screen and natural reflection of the glass. Then use the distort tool and feathered masks to corner-pin your new video into the screen and warp it to match. Then you change the blending mode and opacity so the glass reflection comes thru in the new video, and that sells that it’s coming out of the TV instead of being pasted-on.
Why I would use the randomly-flickering white or bluish-white as an on-set “practical” effect is that, once the screen gets covered, the footage under the mask will still throw ambient light around the set the same way your finished replacement video would, a “3-d” effect that would cost you time and work to replicate in post, when you can get it for free on set as a “practical” effect. The TV is a practical light source on your set.
Again, it’s about a subtle yet key detail that “sells” the replacement shot. You may not, as a viewer, understand consciously why it works better, just that it does.
When you shoot the over-the shoulder from behind the TV reversals of God watching, you can use that same flicker source feeding the screen as a keylight. If God wears glasses, you’d better run the actual replacement footage full-screen on the TV set if you can.