possibilities for a refund from pre-repairment

Earlier today, I requested apple for a battery replacement so i paid the money and all, and now theyre going to send me a box that i can put my phone into which i'll then send to them. However I just found a third party company that is big and is known for fixing iPhone battierries which offers it for a cheaper price. Is it possible to get a refund for this so that i can have my phone battery repaired on the other company instead?