One does have to be careful when issuing any sort of refund because they are not reversible. If it were not this way then sellers who didn't want to refund a buyer would create the refund, get the notice that a refund was sent to 'prove' it, then turn around and reverse it to keep the money. There is nothing for eBay to do in this case as the buyer was fully refunded.
I had this happen to me once and I immediately sent a message to the buyer explaining what occurred. Luckily that buyer was understanding and agreed to pay me once more. I then sent an invoice via PayPal for the correct amount, which they paid. So, I wasn't out anything and buyer received their item.
You can do this, but you will need to reach out quickly to your buyer and explain in detail what happened. Don't play the blame game against eBay or anyone, just own up to this being your error and hopefully your buyer will be understanding. Best of luck to you....
