How likely is it to remove/loosen iPhone back glass without a heat gun?

Have you thought of taking it another Apple service provider to see if they might process an exchange under warranty? Sounds like it could be a manufacturing defect not caught by quality control. You're not obligated to take it back to the store where you purchased it for warranty service. Ideally I'd recommend an Apple Store, but you didn't state what country you're located in.

Viikkah wrote:

Unfortunately I live in Finland, there’s no Apple Store. This is so frustrating.

I prefer Apple Stores because they provide evaluations for free, and generally don't charge unless there's actually some sort of part being replaced. I've even gotten a few courtesy fixes, such as the time someone fished out a SIM card that my wife inserted without the tray, as well as a replacement key for a Mac. I've heard of some Apple Authorized Service Providers that charge a diagnostic fee regardless of what happens, even if service is denied.

However, if there is a manufacturing defect then you have every right to have it evaluated for replacement. If you can find another Apple Authorized Service Provider, they might be able to help.

The only way you’d know if there had been damage was if the device now malfunctioned in some way. As long as it operates normally, then there is no evidence that any damage was done.