A bunch of sensitive eyeballs in here. You must not have to deal with the same Apple Stores I have had to deal with. The ones here don't just roll out red carpets and think that your rear-end tastes like cotton candy.
I had a phone with AppleCare+ that had never been used before. I dropped said phone and the back glass broke. I had to DEMAND that they replace the device with a replacement unit when the back glass was broken. They said that the back glass was not covered under the AppleCare+, even though accidental damage was covered, and that it was impossible to replace the device. They stated that there was no such thing as an out of warranty replacement option either; my only option was to buy a new phone.
You're damn right that I DEMANDED they fix it (by replacing the device) and you're damn right that I got corporate involved with them too. I ultimately got to pay my $99 replacement fee, used one incident of my AppleCare+, and went on about my business like I should have been able to from the beginning.
So yes, you probably will have to go into the store and demand that they replace the screen a second time at their cost. You think that they're just going to start swapping parts and taking phones apart for free? If so, let me know where my plane ticket needs to take me the next time any of my Apple products need service or replacement.
Anyway, hopefully OP is able to get it properly resolved, but I would be demanding that it be fixed.
DEMAND! DEMAND! DEMAND!