I had the same problem because I installed tthe battery connector cover upside down.

Just flip it and screws will magically do their job :)

Just did this, the strips on my 7 years old iPhone 6S were impossible to take out. I know that's absolutely a bad idea but being the battery completely discharged i got rid of it with brute force and installed the new one with no problems.

On the other hand, I replaced my iPhone 12 Pro's one and while the strip worked perfectly I have to deal with a warning I can't remove.

Don't attempt this withou changing the display's adhesive!

Everything went fine with the iFixit battery but now I have to deal with an "Important Battery Message" which I can't delete, and the badge number over the settings icon.