I know the rules, but the recipent of the book either doesn't know the rules or doesn't like them. 

Admits book damaged by USPS, but keeps pushing me for a credit. 

What would you do?

If he feels that the wrapping contributed to the damage, then the rules say he can ask for a credit back.  Otherwise you can copy and paste the info from the help docs on this for him, and/or tell him to contact a tour guide to ask about the rules on this.

First, I'd think about how I packed the book, if that's part of the complaint. Was the packing the cause of the problem? I'd refund if I thought I didn't wrap as well as I should have.

If you think your packing is fine, then I'd decline the refund. There's more of the rules here...

USPS Damage

A book is considered Damaged by USPS if it was damaged in transit (while in the mail).

• This is usually just bad luck
  • Even the most well-wrapped packages can get mangled by a postal sorting machine
  • We have tried to divide the risk fairly between the sender and the requestor:
    • If the sender gets the book back damaged, the sender assumes the risk: she should contact us to cancel the request.  The requestor gets the credit back when we do that, and the sender does not get credit unless she used PBS-DC or PBS Printed Postage
    • If the requestor gets the book damaged by USPS, the requestor assumes the risk.  The requestor does need to mark the book received and does not get her credit back; the sender does get credit in this case.
• If you feel that the wrapping of the book contributed to its damage en route:
  • You can tell the sender this in a Personal Message
    • Please be gentle!  The sender may be new to bookswapping.
    • You can ask for your credit to be refunded if you believe it is warranted.
  • You can share your own tips on wrapping technique, and/or refer the sender to the Help items on wrapping a book.
  • You can also comment on the wrapping in the Comments box at the bottom of the survey portion of the Book Received page, so these details are recorded on the transaction in our records.

I'd just politely tell him or her that if they keep bugging me about it, I'll forward the PMs to TPTB because what they're doing is harrassment. If you've said no, and they can't take that as the final answer, maybe they need to be talked to by someone with more authority than a fellow member.

If you are confident that you packaged the book properly, and you are not planning on giving back the credit, the best thing is always a firm and definite "no."

I've dealt with a persistent person, and the minute I told them "I will not be returning your credit. Please familiarize yourself with the rules and posting guidelines of this site. Please do not contact me again"  they backed off.

Some people see friendliness or a helpful attitude as a sign of weakness. When this happens, they'l latch onto your ankle and gnaw away until you have to whack them on the snout with a rolled up newspaper.

Thanks for the input folks.  According to the recipient damage was clearly USPS, no wrapper & ends burnt. 

Anyway, I pointed out the rules to receiver, and decided to "pay it forward" on this one and refund your credit.