If I change in Outlook the Contact Category by checking another for the Contact, Sync carries it over to Gmail Contact OK.
If from Gmail Contacts check a Group for the same Contact, Sync carries over to Outlook Contact OK.
In Gmail with that Contact detail still Open I click on the Group button little drop down arrow located under Contact name and select Remove from this group, then Sync, the Group is not removed in the Contact record and Sync log viewr did not state there was an update needed to bve performed.
When I then just inserted text in to the Gmail Contact Notes section, run Sync, then the Outlook Contact Category is removed.
So seems like if in Gmail you uncheck or remove a Group to the Contact and touch nothing else Sync does not see a change to just copy everything over to the Outlook contact to update the Category.