Hi Gerry,
I believe you are managing site permission from Alfresco explorer that is not advisable.
From your post, it looks like users are accessing sites folder from explorer too and you dont want them to access.
1)To hide sites folder from end-users who are not invited, You can create site with "Private visibility".
non-admin user can not see private site folder from explorer/repository view and they also can not search from Share UI.
2)Other options is create site with Public and Moderated membership so non-admin user can see only site folder from explorer/repository view not anything inside that site folder and from share UI they can only search site and request to join that site.
Hope it helps!