Is your Zoom done in production (real camera zoom) or are you planning to do it in post?
If it’s a real camera zoom then Dave’s suggestion is the way to go.
For a post production zoom you can work your way backwards- figure out how long you need the zoom to be (the longer it is the more you will notice degradation in the green screen plate). Go at the end of the zoom on the time line and scale up the image with the tv to fill the screen ( the whole tv screen, edges and all) and set keyframes. Use Corner Pin (under Distort) to match the screen with the video you want inserted and set keyframes. Parent the video layer to the green screen plate, go to the beginning of the timeline and scale that one back to 100%. Go back to the end of the zoom and scale the green screen plate a bit more until you loose the edge of the tv. If you need the video to be completely un-distorted then go 2-4 frames pass the end of the zoom and reset the corner control points for the Corner Pin to match the edges of the image to the edges of the comp. Add an Adjustment Layer on top with a animated Radial Blur (Zoom) to hide the image degradation and you’re all set.
Tudor “Ted” Jelescu
Senior VFX Artist