Buyer opened a return request but doesn't respond to messages.

[letitia407]

A buyer purchased and received 2 purses during a BOGO1/2 off sale.  On 09/26/15 (5 days after she received it) she opened a return request, without contacting me, stating one of the items was defective.  On 09/27/15 I responded with a message offering a partial refund to repair the item, a refund for the one item, or a full refund.  The buyer has not responded.  Ebay has said I need to settle this before Oct 1, 2015.  What do I do if the customer doesn't respond?  

Thank you for your advise.