I think I may have found the answer to my question.
https://support.na.square-enix.com/f...+factory+reset

If you have already completed the registration process, you will have to remove the Software Token before deleting it.

Please visit the following page for more information on how to remove your Software Token.

How do I remove the Software Token from my Square Enix account?

After the Software Token has been removed, you can delete the application and re-download it to complete the re-installation.
Though it seems they never provided said "following page." >_>