If you are talking about the back layer of the backlight sheets, I believe it is stuck to the aluminium backing itself. Most sheets are swappable from another assembly (which is a nightmare to do without scratching or getting dust behind), but the plastic bit is not.
I would say your best solution is to buy a new assembly at the moment, or just see what it looks like with a new screen (will usually cause white backlight marks in the background). It sounds like you have taken out all of the backlight sheets at this point, so even if you manage to replace the backing and the backlight sheets, you will definitely see dust and scratches behind the new screen, so it won't look nice.
If you want it to look good at this point, buy a new screen :)