Ran across a problem today where a legit Office 2003 got flagged as being not legitimate, displaying a nag screen each time an Office application got started. The Office Genuine Advantage update (short: OGA) is an update installed with Microsoft Update, similar to the Windows Genuine Advantage update (short: OWA). While Microsoft flags the update as not uninstallable, there are ways to get rid of the update anyway.
Uninstalling the update is your best bet, and can be done from a (elevated) command prompt.
An alternative to uninstalling OGA is disabling it in Office. This can be done quickly using the registry editor.
The least preferred method is actually deleting the files of OGA.
Avoid using other third party tools such as hacks or cracks. They are unnecessary to solve this problem and usually only compromise your system's security.