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I got my iPhone battery replaced at Staples (it was less expensive to have them do it than to do it myself), and everything was fine at first, but now my phone rattles if I shake it. I assume the battery has come loose somehow. My phone is still working just fine. Everything is functional. How serious of an issue is this? Can I leave it as is, or will it cause more problematic problems later?

Thy must have forgot to apply adhesive if you want you can do it by yourself.iPhone 6/6s/7 Battery Adhesive Strips

the battery is held down with glue, bring it back to the store, they will re-glue it.