Hi Marvin,

If you are referring to this(http://take.ms/sSUca), it will display to users that are super admin, event owner, event admins, or when there are filters/hashtags belonging to the event.

You can template override this file if you want to disable it but it will also affect normal events and other cluster events, not just group events.
JoomlaFolder/components/com_easysocial/themes/wireframe/events/item/default.php