It is definitely not a county, but a provincial administrative region. If it is a municipality directly under the central government, it refers to the city where the card is located. If it is not a municipality directly under the central government, it refers to a province.

China Construction Bank, for example, has a preferential treatment for local banks to waive the handling fee for the overpayment, which means that there is no handling fee for the overpayment on the credit card of the province (municipality directly under the Central Government) where you handle the credit card.