If the case opened was not As Described,which requires you to provide a Reply Paid Label, you had no choice as if you didn't deal with it buyer could ask ebay to takeover all at your expense.
You are now in a fix, as we would never recommend a buyer to close a case on the promise of a refund. Once the case is closed, there is nothing to enforce any refund partial or full.
If buyer realises this they may be reluctant to cancel.
