I released a game recently and I was supposed to set a discount for the first seven days after launch, but since I had to fix an urgent problem with the Steam release I was not able to set the discount on Itch in time and two people bought the game at full price.

Is it possible to give them a partial refund so that the amount they paid corresponds to the discounted amount?

If you have the collect by Itch mode, from what I've seen in other posts, the answer is no.

In similar cases, the answer is that the person must request a full refund of the payment and then make the purchase again, with the new price.