I've never used 3rd party ink so I don't know if there are any ill effects. Some HP printers know when you've refilled a cartridge and won't print with it. You might want to research if your printer does that too.
I know with my Canon 100 pro, if I want to refill my own cartridges, I need to buy a "chip resetter" so the printer will know how much ink is in each cartridge.
