When you click on "Resolve", it will open a notes box. Here you can enter that you've put a case in, Athena ID, that you called them back, etc., whatever notes you need to add. Then click on the "Resolve" button to save the note.
All group members can then see at a glance that a message has been handled without necessarily having to go into Athena to see if anything has been done (or look elsewhere), or having to ask if a message has been taken care of.