Someone took a permanent marker and put a line on the outside edge of the book (parellel to the spine on the top edge of the book).  Is this OK to post? 

Welcome to PBS.   That is considered a remainder mark and yes it is postable. 

"Page edges: remainder marks are OK.  A name written on the page edges is okay (if it does not bleed in and obscure text on the text pages)"

see help docs -Book Condition Criteria for 'Swappability' at PBS

Thanks for the clarification!  I read the help docs but had never heard the term remainder mark before, so I wasn't sure exactly what it was.

As always, people are so helpful here (and fast to respond!)