Who should pay? Mechanic broke piece

Maintenance/Repairs
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2

Door handle trim especially plastic gets very brittle when it ages. Since your vehicle is about 17 years old then brittle is probably an understatement. I would just pay for the part and find another shop if this one no longer suits your need. The shop could have paid for the item as a good will gesture but some shops do and some don’t. It’s your call.