There will be a password in China, so the signature is not important. So be sure to sign it. Now some credit cards don't have passwords. If you don't sign, you will inevitably suffer when you meet a conscientious salesman.
If LZ's credit card requires a password, you can ignore the signature error. If you don't need a password, you must ask the bank to reissue a card (the fee varies from bank to bank), or apply for another credit card from this bank and cancel the previous card (free of charge).