For most users, the practical choice is to buy or turn off HP cartridge protection (if your printer allows it) rather than fighting the chip.

While you can perform a "cold reset" on the printer’s internal memory (the formatter board) to clear error logs and restore factory settings, this rarely resets the external chip on the cartridge. The smart chip is a standalone memory device. It does not easily accept "overwrite" commands from a PC because that would defeat the purpose of copy protection.