How can I refund shipping fees to a customer? Can BorderGuru do this?

Your customers pay the entire amount that BorderGuru calculates for them (shipping + import fees) to you at checkout. This adds to the convenience of the international shopping experience convenient for your customer, as they only have to remit one single payment.

Because the customer's payment is to you / your shop, and not BorderGuru, BorderGuru cannot issue any refunds to the customer. 

If you want to send refunds, you can simply use the refund functionality of your shopify backend.