Non-HP supply Installed is a typical scare message from HP. With all remanufactured or refilled toner cartridges, the original chip must be replaced with a new one.
As your printer cartridge has a chip to communicate with the printer, this message is just a scare message from HP to convince you to spend more on a new HP brand cartridge as HP does not make any money when you choose a refilled or remanufactured product. Even if we refill an original HP cartridge, we have to replace the chip with the compatible chip as HP does not sell chips.
To clear this message, you have to press the override “select button” to accept this message. Once acknowledged, you will be able to continue to print. The select button might also be called an OK button, and it could also be a large green/grey button on your printer. Press Ok and continue to ignore the message. Once you ignore the message, you will be able to continue to print.