You would need to check the individual permissions set for the group hub owner role and it allows them to add/remove labels. By default, it doesn't look like the Owner role does on my instance (Which seems kind of silly - By default group hub owners can delete the entire hub I believe).
Just change the permission on the role and you should be good.
Some of our group hubs use labels and we have to manually adjust the permissions of the group owner (and the members role, so they can add labels to posts) for those group hubs - just as Stan says above.
We also take away the permission to delete the group hub, since I don't want someone doing that by accident!
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