Confirmed the invite notification is logging fine, but it's not displaying. You can see the notification logged within CB Activity > Notifications. You'll see notifications with an asset of groupjive.group.GROUP_ID.user_invite for example. So this is likely just a display issue in GJ it self not correctly parsing user_invite access. This normally should be ".invite" instead of ".user_invite", but both are supposed to be working. Have added a bug ticket to fix.
forge.joomlapolis.com/issues/7808
You won't need to make any changes to the system action or GJ. Once fixed you'll just need to update GJ and the notifications will display.