BuddyPress.org

I’ve been looking for a solution and found a lot of dead ends….

Possible hook. Though Not sure if it works.
https://buddypress.trac.wordpress.org/browser/tags/1.5/bp-themes/bp-default/functions.php#L112

There is this unanswered post
https://buddypress.org/support/topic/how-to-disable-join-group-option-on-public-group/