Try to switch them around, I have a case where the top screw won't screw into the lower hole but the lower screw works with the top hole. Got to love these Chinese tolerances.
Heating up the case a little might also help, not too much so you won't damage the rubber components attached to the case. I had a case where the hole was clogged with gunk from the strap.
Try with a new screw a couple of times, sometimes it's hard to catch the correct thread.
Only force as last resort, take the strap out and spin the screw with pliers to prevent screwdriver slips. It'll most likely mess up the thread though. It only worked for me once.