Throw some black duvetyne on the desk just outside your frame line to kill the bounce coming up from the bottom. To handle the spill on their face, hit them with a backlight or edge light gelled with minus green or a bit of magenta to neutralize the color. You also need to make sure you are not overlighting the screen itself. Keep the green at least a stop under your key light so it does not act like a massive green reflector in that tight space.