Here's a similar post with a response from pbs below:

http://www.paperbackswap.com/Paperback/topic/231390/

The reinforced covers do change the binding type - either to "library
copy" or another term is "turtleback" - these are types of hardcovers.
Members who request paperbacks sometimes specifically want paperbacks for
good reasons (for example, softcovers are much easier for arthritic hands
to hold).  

If you have a book that was rebound in this way so that it is no longer a
softcover, you should ideally create a custom listing for it using the
"post a book without an ISBN" option, to avoid surprising the receiver.
If you post a library-rebound book using a listing that says "paperback"
you do risk a problem swap.