Yeah, it must be polarization. Both pics are from the same scanner, but the left one is a stack of the background, the LCD panel and the foreground, while the one on the right is only the background. When I just stacked the foreground on top of the background without the LCD panel, it was extremely dark.
Okay, so I guess it's not just a regular plastic but some kind of polarizing sheet? I guess it would be really useful in this case if MAME could handle each layer's transparency/reflectiveness properties individually.
I've uploaded the current version of the combined backgrounds, anyway: folder
I've found that the Game & Watch games seem to look better with "Multiply" layer types while this one works better with "Darken" types, although the layers may be looking a bit more transparent than they should in Thief.
In any case, all the individual layers are included in their respective folders in case that somebody can find better ways to combine them or can make some shaders that take care of them altogether in a cleaner way: Folder with all cleaned background layers so far.
EDIT: By the way, I think that VDF games could also benefit from overlays/shaders. Have a look at this: