Don't send "add a message" outside of the group for invites

We are attempting to use the group feature as a one stop shop for calendar invites for our team. Our situation, we have several office team members that coordinate field staff. We get invites from numerous staff outside our "group" so I want to make it easy and just give them all one email address so they don't have to worry about who to contact. The hope was using group calendar to solve this. I noticed that the "add message" feature and thought this may be a way for our team to let other members know they have processed and forwarded the invite to whomever else needs it (field staff). When I tested it though I noticed that the "add message" also goes back to the person sending the invite even though they aren't part of the group. Is there an options somewhere I'm not seeing to keep this response to only those in the group and turn off external responses for invites? Thanks. Other suggestions on how teams manage