Reducing green spill is a four-fold solution, I've found...
1) Put the actors far enough away from the screen.
2) Back to kindergarten! Remember the color wheel? Use a magenta gel on your character's kicker/backlight. Magenta + green = black, so that should cancel out any green spill you'll be getting. Sounds wonderful, but in reality doesn't take it all.
3) Find out what in particular is reflecting. White reflects way more so than black. Try to put your characters in patterned clothes, warm colors, or dark colors.
4) Use a good screen keyer with a spill suppression feature. It will work to subtract the green while not making those pixels 'invisible'. If this isn't possible, create a matte around your actors and then dial down the saturations on just your greens.