Thanks, Jim, for your reply. I deleted Groove.exe because I was annoyed by the server authentication message. Even if not, your response is not helpful, as I won't delete anything in the OS that I don't know what it is. I expect from Microsoft Windows Update
utility that it delivers what I purchased and payed for. I'm not willing to jeopardize sanity of my Office 365 that otherwise runs fine; I make my living from using Windows and Office, not from repairing installation.
However, I found it on my other laptop, and Groove.exe is Version 16.0.6366.2036 indeed. Going to Control Panel on the main laptop, there is no Microsoft Office Subscription. however, on 'Programs and Features' have four language versions of the Microsoft
Office 365 Small Business Premium, en-us, de-de, it-it, fr-fr, all updated 2.1.2016, plus "Korrekturhilfen 2013 Deutsch" and "Proofing Tools 2013 Italiano". the latter two I wonder whether I should uninstall. There is nothing like a Groove or OneDrive apps.
Finally, I cannot see how deleting credentials stored in a cache should change server authentication protocols on server side. I regularly delete cache using CCleaner and Disk Cleanup. I know the URL of my.sharepoint.com but trying to reconnect the Groove
client to it didn't help either. It looks to me like the server needs repair, not the client.