If your buyer opened a case under eBay's money back guarantee and you both agreed through the case to a partial refund, that's the end of it. He can't make any further claim.
If you just agreed this privately it's between you and your buyer. Normally I would advise you to ask him to open a case and deal with it correctly under eBay's money back guarantee. However, if he does so now you may be required to refund the whole payment. eBay won't take account of anything that you may already have paid the buyer privately, not through eBay.