I sent a book that the receiver marked as....

"Thanks for the book. Unfortunately, it was damaged by the Post Office. However, it wasn't damaged beyond repair, so I can still read it." 

PBS.... "it might be reasonable for you to refund the credit,"

How do I do that?

You do not need to refund the credit for damage by USPS if it was wrapped well.

From the Help Documents: Damage by USPS to a well-wrapped package is considered bad luck. The risk of this is split between the requestor and sender in the following way:

• if the book does NOT get to the requestor (= the requestor gets an empty wrapper or the book or wrapping is returned to the sender) the sender absorbs that blow and loses the credit
• if the book DOES get to the requestor (even if damaged), the requestor pays the credit for the book.

However, if the wrapping was truly inadequate for normal USPS wear and tear (such as the wrapping did not cover the entire book), and thus may have contributed to the USPS damage, then the requestor can ask the sender to refund credit, since the damage in that case would have been avoidable, and not simple bad luck.

But to answer your question, to refund a credit, (also from the help documents)

If you need to refund a credit from a swap for a book you have sent, you can click the

button on the Request Details page (accessible from the transaction for the book in your Transaction Archive).

To do this

• Go to your Transaction Archive: http://www.paperbackswap.com/members/transactions/index.php
• Locate the transaction in the list.
• Look on the right side of the transaction for the Request Details link -- click that
• On the Request Details page, find the Give Refund button to the right of the cover image on the transaction. Click that. Confirm the refund if a box pops up to ask you to confirm.
• That's it!