Drew,
The phenomenon is called 'coupling'.

Woven screens perform slightly better than perfed in this regard, but even an inch of space between the baffles and the screen will keep the perfed screens from coupling to LCRs. You will want a lot of breathing room for subs behind a screen, regardless of the screen material.

The best advice to prevent this is to space the screen off the baffles of the speakers (or the wall, in this case). Use some strips of MDF or something, paint them black, or get some black velvet or veltex material and they will not even be visible.