Customer Refused a Delivery

Got an odd one. Customer ordered a product and selected Second Day Delivery option

We sent it via DPD and in the words of the customer “I thought I received a strange package. The postman asked me and said it wasn’t mine and I said no.” So they refused a delivery they’d ordered just the day before.

It’s now on its way back to us according to DPD. I’ve no issue with refunding once we get it back - I assume I would not have to refund the Second Day Delivery charge?