I keep an active List of "Contacts to remove" for contacts which HubSpot automatically adds to my CRM based on email conversations. Any contacts with a particular domain (eg: UPS.com) are auto added to this list and then I go in a delete these Contacts from my CRM.
I want to use this same list to filter my Conversations in my Inbox.
Stated another way - if Contact is on a specific List do not show them in my Inbox.