Buyer refuses to accept refund and demanding compensation

If the buyer refuses your offer of a full refund on return, then there is nothing more you can do. Not sure how they expect to be compensated, or what for, but I suggest you do not get in to any further discussion and leave it in their court. You have done the right thing, and it's now up to them to do the same. In the meantime, don't stress, forget about it. Under no circumstances should you agree to be bullied in to a full refund + let them keep the item + compensation. It's not the way things work.

You made a mistake of offering an "immediate refund", that shows your are inexperienced and easily scammed (not saying they are trying to scam you). You should have asked for more details, eg. Photos or video of the item, better still if they have a video of the item getting unboxed, when was it delivered, how was it delivered, has a signature been obtained, etc etc etc. Also told them to wait for you to send an enquiry to the courier company. 

Finally, when you have had enough proof that you have been pro-active in resolving the issue, just ask them to open a dispute with Trade Me and stop all communications with them, and wait for Trade Me's professional dispute team to handle that for you, and explain to Trade Me's dispute team that you have done your best to resolve this issue but they are not accepting your resolution, you need Trade Me's help.

Make it as hard as possible for the buyer before offering a refund.

Hi Fran, thank for posting - sorry to read about this situation. We wouldn't expect a buyer to be refunded without returning an item. I agree with Gary - you've done the right thing and met your responsibilities here. 

We don't encourage any trader to make anything as hard as possible for another trader, however Arthur is right that you can encourage them to file a Dispute report if they're not satisfied with the offer of a refund upon return.