Apple Software Update keeps telling me to update iTunes when I have the latest version already?

Try repairing Apple Software Update from the Programs and Features control panel, then uninstall it before trying to reinstall iTunes. If it won't repair try the Microsoft troubleshooting utility mentioned in note 1 of the following guide. If it still won't uninstall you can remove all Apple components that will uninstall then use the steps in Install missing components to install everything apart from Apple Software Update.

For general advice see Troubleshooting issues with iTunes for Windows updates.

The steps in the second box are a guide to removing everything related to iTunes and then rebuilding it which is often a good starting point unless the symptoms indicate a more specific approach. When reinstalling right click on the downloaded setup file and use run as administrator. It may also help to temporarily disable any non-Microsoft anti-virus.

Review the other boxes and the list of support documents further down the page in case one of them applies.

The further information area has direct links to the current and recent builds in case you have problems downloading, or want to revert to an older version if the current one won't work properly for you at the moment.

Your library and device backups should be unaffected by these steps but there are links to backup and recovery advice should it be needed.

tt2

When you reinstalled did you right-click the installer and use Run as administrator? Have you tried running Apple Software Update as administrator? My guess would be that some sort of permissions issue is preventing ASU from updating its record of the installed version.

tt2

If you are working with Windows 10 you could uninstall all Apple software and then reinstall iTunes via the Microsoft Store.

tt2