Ok, but, I think, mine is not metallic. So out comes the screwdriver to open mine again and here's the deal...
The white part in the photo that I thought was double-sided adhesive is actually the back of an adhesive sheet of that metallic aluminum(?) stuff.
The little rectangle of aluminum facing the interior is part of that same sheet folded over, providing continuity to the whole sheet. And the little spring makes contact with that little rectangle.
The clear plastic is apparently just to cover the adhesive so stuff doesn't stick to it.
Now, why in the world they wouldn't just stick a big square of the stuff on with the aluminum facing the interior, and do away with the whole folding-over and covering w/plastic thing, I don't know. So the mystery continues.
But, the general purpose of it as a frequency shield makes sense. And hopefully it isn't too critical if there are a couple little tears in it as mine now has, hehe.