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Is my earpiece suppose to move back and forth on Motorola turbo 2

Most likely not. especially if it only started doing that and didn’t always do that before. if it came loose this guide may help Motorola Droid Turbo 2 Earpiece Speaker Replacement

I think you’re referring to the little bar that covers the opening. Mine was loose for a long time, and finally fell off when I wasn’t looking. It doesn’t appear to effect listening, but I’m worried something will get into the openings.