green screen

You don't need anything but Mocha. You adjust the surface so that the rectangle matches the screen by just guessing where the top and bottom left corners of the screen are, verify that the track looks good in Mocha bu inserting an image or something like the grid, then you apply Corner Pin to the replacement layer below the footage instead of above, then use Keylight to cut a hole in the top layer. You'll have to animate some masks to hold out the X's that were added to the screen. If you ever need to shoot something like this, tracking markers are completely unnecessary and the greenscreen actually makes it more difficult to do a believable composite.

Here's what the Mocha Screen and the Comp would look like:

There are dozens of tutorials, good ones, on the Borris FX site for Mocha and Mocha AE that detail this workflow. If there were no tracking markers on the screen there would be no need for the Outside Mask in Keylight. I've tried to show you everything you need to do.

Boris FX Mocha YouTube Chanel

Stick with the Boris FX tutorials because there are a lot more incomplete and misleading tutorials presented by enthusiasts on YouTube than there are good ones by professionals. Vet Your trainers. 

Here's a good intro by Evan Abrams: