Calls to missing system folder files

Hello,

Our client’s web host contacted us recently regarding our EE2 installation on a shared server - letting us know that there were an abnormally high amount of calls to nonexistent files being made from our site on a “per page” basis - causing strain on our site as well as other shared sites on the server.

They sent a text file containing a list of extraneous file calls, which can be viewed here: http://pastebin.com/gPfKvGd7

There seems to be a loose pattern of file/folder requests, like various filename casings (api.php and Api.php), but also repeated items in sibling folders (like /libraries/Addons.php occurring in multiple folders).

Does the pattern look familiar to anyone? Is there any reason why EE would be making these calls to nonexistent files on each page load?

Any tips or advice would be much appreciated.

-Stumped