Today I received a notification from a member that I sent a book to saying the book was stained and had markings.  I am in distress as to whether I should return her credit.  The book is an older, out of print book and I skimmed through it to make sure it   was able to be posted before I posted it.  Since it was a notably older book I felt that anyone who requested it would understand that it isn't going to be in the most pristine condition.  I always look for water damage and I never saw any staining or markings in the book as I evaluated it.   I feel bad that she was unhappy with the quality of the book but if I felt like it was in poor condition I never would have listed it.  Should I return her credit?  She didn't ask for her credit to be returned but I wonder if I should return it anyway.  What is the general way to handle an issue like this?  

Well, it depends. It does sound as if you didn't check the book particularly carefully before sending, so it's not out of the realm of possibility that you missed something. She didn't ask for her credit back, so you are certainly within your rights not to return it.

ETA - it's also perfectly okay to ask for pictures.

It's a bit of a pet peeve of mine when people say that a book was in good condition for its age, as age and condition are separate issues.

I think since the requestor did not ask for a credit to be returned, a credit return is not necessary in this case. 

If the transaction was marked "Received with a problem -- Damaged by sender" then the default is to request a credit refund. The requestor had to uncheck the box, so it's very likely she doesn't want the credit back. 

It is always up to you whether you want to return a credit. If you are confident that the damage was not there when you sent it, and your packaging was adequate, then you can refuse a credit refund without guilt. 
Another option is to ask for photos of the damage. 

I hope this was helpful. 

Help Docs: 

Damaged by Sender

• You will be required to describe the book condition problem in a text box - the text you type in will be included in an email, and sent as a Personal Message, to the sender.
• You will have the option to request a credit refund - this is checked by default for this problem type.  If this option is checked, the email the sender gets will include the request for a credit refund. If you uncheck this option, the email sent to the sender will NOT mention or request a credit refund.
• If this was a Wish List book (and there are no other copies available), you will go back in your previous place in line for the book.  If there are other copies available, the book will go onto your Reminder List.

Just because someone didn't "demand" their credit back, doesn't mean it isn't the right thing to do or that they aren't expecting it.  If pictures can't support the supposed "damage" and you feel certain it was postable, then you are not obligated to return the credit, but be advised that the recipient may possibly never mark the transaction as resolved.

If I'm not planning on reposting a book and it arrives with a problem, I don't ask for my credit back. And, honestly, I mean it. I think we should really assume people mean what they say. If someone wishes to go above and beyond and return the credit, that's great. But I really don't think they are obligated in any way.

I agree with the previous posters who mentioned requesting photos -- not everyone is able to provide them, but it would help you to see what the other member is referring to, I think.

Whether you decide to give the credit back or not, the one thing you must do, that members sometimes neglect to do, is respond to her message, even if it is to only politely state that you disagree.  PBS requires this sort of communication, and takes a dim view of members who do not respond.  Sometimes folks don't know what to say, so they say nothing, and that's the worst path to take.

So, apologize for her frustration, ask to see any images she might have (use a photo sharing site like PhotoBucket and she can send you the link(s) to the image(s)) and go from there.

Thank you for your replies.  I certainly didn't notice any damage or writing on the book when I checked it out.  It is likely that my name was on the inside of the book and I missed it and perhaps that's what she is disliking. The requestor did not ask for her credit back but I know I need to respond and apologize but I'm trying to figure out how to word it without being defensive and suspicious.  

That said, your name in the front cover is acceptable by PBS posting rules. That would be a non text page.