For anyone that stumbled across this post. I figured out the solution.
I had to disable OWA completely for the user under the Exchange Admin page and re-enable it.
After that, the signature portion under settings reappeared (if you have the Email Signature checked).
Then, I removed her signature and for some odd reason, I had to re-disable OWA again and re-enable it for the email signature portion under settings to disappear (after unchecking the Email Signature box.)