If you click the Options button in Time Machine preferences you can specify items to exclude from backup. I’ve found it can be impossible to remove those excluded items; even deleting com.apple.TImeMachine plist (preference) files didn’t remove the item. It seemed to go away, but on return it was back.
It appears to be a permissions problem in Mavericks. I’d added the exclusion from a non-admin account, and I was working on Time Machine preferences from my admin account. I had to switch to the non-admin account to remove the item. I don’t know how to fix this if the originating account no longer exists. I don’t think Time Machine is storing this string in its preference file.