I just received a book with little indentations, kind of like braille dots, along the upper edge of the cover and also little tears along the edge that go through about 8 pages.  The book is still readable, but I wouldn't repost it. Otherewise the book looks pretty good.  Is this reason enough to ask for a credit back?  I had planned to keep the book anyway, but it's the principle of the thing.  We should only send books that can be reposted, right?

Sounds like kitty not mousey, IMO.   You should let the sender know about it, in case she has more books like this--and keeps her PBS books in a cat-accessible place.  I don't think I would ask for credit back unless it was pretty bad damage; she may not have noticed it before she sent it out? and if you plan to keep the book, you aren't losing the credit you would get by reposting.

edited to add: I would def mark received with a problem, though, in case this sender is careless...this will make the issue part of the record if it is a habit with her.

Mice don't let little tiny dots.  It probably was cat teeth that made the marks.  Mice chew, not bite & leave holes.  I got one from the used book store like that.