To correct a Permanent Resident Card, I-551, you must file Form I-90. If the error was the fault of the USCIS, you do not have to pay the fee. If the error was your fault, you do need to pay the fee.
Note that the bottom of page 1 of the Instructions to the I-90 says:
‘A replacement application based on administrative USCIS error must also include an explanation.’ Therefore, please attach to your I-90 your incorrect Permanent Resident Card (Green Card) and, if possible, a photocopy of the original application that you submitted that had the correct information on it as proof that your original documentation was correct.
On the Form I-90 itself, under ‘Part 2: Application Type,’ you should mark ‘2.d.’ as the reason for filing. ‘2.d.’ states: ‘My card was issued with incorrect information because of USCIS administrative error. I have attached the incorrect card and evidence of the correct information.’