if a buyer requests a refund because item doesn't fit, do they have to prove it to get a refund?

[beakychew]

One of my sale items is toothbrush heads for electric toothbrushes. In my listings I detail which models the heads will fit.

A buyer has submitted a refund request based on the item not fitting.

I'm assuming that the buyer bought the right type, since these are the most common type of heads for this brand (by far).

I have sent a message asking to see evidence that the they don't fit the toothbrush and the buyer has not replied. My message was sent through the Return Request, and when I didn't get an answer for 2 days, I also emailed the buyer to ask them to read the message and respond. Still nothing.

Ebay is asking me to resolve the refund request by today. 

The buyer will have had to unpackage the heads to find out they don't fit, so if they are rturned, the item won't be saleable, even if they are perfectly good.

I have also aasked the buyer to advise whether they would prefer to pay for postage for the return and be refunded, or have a prepaid satchel supplied. Also no reply. 

Am I obliged to offer a refund? Including postage?