Filtering by contacts that global bounced

HubSpot charges our clients for the number of marketing contacts in the system. However, when a contact bounces globally for all of HubSpot, there is no prooperty on the contact record that indicates that this has happened. Thus, there is no way to trigger an automation to remove that contact as marketing contact. I have a client with 200,000 contacts and I an unable to filter database in any way to ascetain who can not be sent emails but is still a marketing contact.
This smells of unfair pricinig practices to me.

Let’s get this fixed.