Remember that this is a business decision. It's up to you if you want to try teaching the customer a lesson, but you will probably spend a lot more time on this than the amount of the dispute is worth (not to mention the emotional toll), and chances are the customer won't change her behavior even if she loses.
I tend to agree with this at this point, since it's so far after the fact. Just send your info in and see what happens, because that's really all you can do, but if she wins the dispute keep this in mind as a pain in the butt learning experience.
Taking no credit cards is the only way to avoid this these days.