HP I assume don't let you reset the counter as like anything the cartridges are subject to wear and tear giving them a limited lifespan?
You can buy both new and original cartridges online really cheap nowadays so in my mind that just makes more sense than refilling at home. HP actually sell their cartridges online at
findmysupplies but at a lot lower prices than in the shops and there are plenty of places that sell refilled ones.