If an agent or lite agent has notifications turned on for mentions they get an email that is similar to:

After a discussion around why replying to the email notification was creating new threads I was told that its not actually a feature that intercom supports.
My suggestion is to allow replies to the notification, like it is suggesting to the receiver. Short term, I would ask that the “Write above to add note” goes away and a message saying NOT to reply to the email is added so there is less confusion.
Our lite users are not in intercom unless needed so the alert is a bit confusing.