These "recycled" cartridges offer an exacting but cheaper alternative to original cartridges. In essence, these cartridges can be used in place of the expensive original cartridges, the only difference being that they have been used once and then carefully reconditioned, before being refilled with a high-quality compatible ink. So, now there is a cheaper "compatible" alternative even if your cartridges are the type containing a printhead, like many of the HP models.
You can find the Remanufactured Cartridges for your printer by clicking on the printer make Logo, selecting the model from the drop down list and clicking "Continue". Remanufactured cartridges start with IKR.