You need to bear in mind that groups are cumulative, so each additional group a user belongs to means possible additional permissions but NEVER fewer.
You can remove the the default additional permission (Show_group_members) a "Registered" user has, but you can't take away the permissions they will be left with by virtue of their membership of the "Anyone" group.
You can delete the default permissions that "Anyone" users have (View, Create_topic and Reply) and give some or all to "Registered" or "Member" users, but a "Member" will ALWAYS have those permissions that "Anyone" and "Registered" get and a "Registered" user will ALWAYS have those permissions that an "Anyone" user has.
The best you can do to create a "low level registered" user, is shift all your existing "Members" to a new "SuperMember" group, and your existing "Registered" users to the "Member" group, shifting permissions accordingly, and reduce the permissions that a Registered user has.
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