it should'nt affect the screen protector, i also have a leather type case, using it for my HTC 7 Mozart, you can see the photo of it next to the pouch, it also have a ribbon inside to pull out the phone, it's very cheap, i paid about USD 5 for it in hong kong, and should cost about USD 1-3 in china.
they have them in many sizes, i mean like 2-3mm differences, in width, depth or the length.
I can take more photo's if you want.
Samsung Galaxy Note III LTE N9005
Samsung Galaxy S4 Mini Duos I9192
Sony XBA 3
Sony MDR EX600
Sony MDR EX800ST