Well that was a complete waste. I drove an hour to our closest Best Buy and they took one look at it and said because it appeared to have a swollen battery, they can’t touch it and directed me to ship it in to Apple.
I can probably explain why. I have had an iPhone 5 replaced twice for the same issue - battery swelling. It is possible when replacing a battery that it can be punctured. With ordinary dead batteries this isn't an issue. But with swelling batteries, it's an explosion/fire hazard.
Apple has a special facility with special tools and specially trained techs that they ship devices with swelling batteries to. Best Buy is not so equipped.
Apple simply replaces devices because of all of the above.
What you should demand though, if they do not give it to you, is that you are only charged the cost of the battery replacement. Both times my iPhone 5 was replaced that is all I was charged.
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Several years ago I had an iPhone 5 that had a swollen battery that was pushing up the screen. I took it to an independent iPhone repair shop and the tech replaced the battery and refitted the screen. Fit perfectly flat afterwards. I still have that phone and it's fine.
Apple salesmen will always push a customer to buy a new iPhone instead of fixing an old one. Find out what the repair will cost and ignore the warnings they give you. They want to sell phones, not fix them
You are very fortunate. Had the shop punctured the battery during the replacement, you may have found that shop featured on your local news because of an explosion and fire.