Upgrade theme when non-theme files are in existing theme folder

Getting ready to upgrade to latest version of Atahualpa.
Am now in version 3.4.6, with WP 3.2.1. I have juggledad's upgrading procedures post.

Had work done by a coder to add a database to my WP site, and the coder added 30+ database-related files (example: page-2417.php) to my atahualpa346 folder.
Here's the site: http://seriousgivers.org/

I know just about enough to be dangerous, so want to check before I make a mess of this:
** I'm thinking that I should move those non-theme files into a new folder, which would be a sub-folder of wp-content. Is that the best way?
** Once I've moved them, do I adjust the WP database so links to the moved files will work? If so, how?
Suggestions will be much appreciated.