Re-reading your issue, I will have to correct my original answer. I assumed this was about false "business use" alerts, however, as you stated: reinstalling fixed this, so it's not a problem attached to an ID but to the installation itself.
In this case, you could remotely fix this problem using a QuickSupport module in order to reinstall the full version of TeamViewer. Please keep in mind, that also a mixed use, i.e. both private and commercial use, requires a license.
I have forwarded your suggestion to our product management. Such ideas are always welcome, although I can not promise when or if this Feature will be implemented, as the decision is based on public demand.
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