Do you have a hand strap on your case/cover that touches the screen when closed ?
I've seen reports of the strap leaving a dirty "imprint" on the screen that you can actually wipe away with a cloth.
I see this on my S4... the Smart Cover window always leaves a rectangular dirty mark on my screen that I can wipe away.
Might be something else though...
Hope you get it solved... it must be like having an injured child
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