Since the functionality for deleting was for the anchor tags and not the containing span/paragraph, the $('a.delFile') was not changed to $('p.delFile').
I'm stumped. I just don't see what I'm missing.
If anyone knows of a website that can offer ColdFusion help that isn't controlled by neurotic, pedantic jerks* (stackoverflow.com), please PM me with a link.
* The neurotic, pedantic jerks are not the owners; just the people who are in control of the "popularity contest".