1. Which membership plugin you are using?
2. This plugin’s group feature does not have any option to add password. Are you creating groups from this plugin? Eg. Dashboard > Front End PM PRO > All Groups
3. When and from where your users are added themselves in groups?

This setup for wordpress page level setup and does not have any impact for group.

By default user can assign themselves to a group from settings page of the plugin. See https://www.shamimsplugins.com/docs/front-end-pm-pro/getting-started-2/group-messaging/

In your website how users assign themselves to a group from signup? Did you change any code for this plugin?
Which group you want to hide from your members? Are your users logged in when they signup for groups?

Thank you.
So now you want to hide some groups from some users, right? Which groups you want to hide (give me group id) from which users (give me those users role)?

Please go to Front End PM PRO > All Groups, then click “Edit” of the group whose id you want to know. Then see in address bar. Please see screenshot attached.

add following code in your theme’s (child theme’s if you are using) functions.php

add_filter( 'fep_get_all_groups', function( $groups ){
    if( ! fep_is_user_admin() ){
        unset( $groups[ 7930 ] );
    }
    return $groups;
});

This group will be hidden for users who are not admin.
If you want to hide for other user also let me know their user id or role.

Let me know.

With the above code users will not see that group in settings page. So they cannot add them to that group. But if you add them to group (from back-end) then they can send message to that group.

Please test and let me know.