Hello @KPater,
Welcome to the HubSpot Community! You are on the right path, as @TitiCuisset mentioned in the post, currently there is not a specific tool for this, but if you have a Marketing Pro subscription you could create a list based on the Activity Properties filters - using the Email Body or Email subject filter, to filter all the contacts who have an email logged with this content.
That would allow you to know which contacts have logged the "e-mail doesn’t exist " reply and to more easily find the newly created contacts that need to be deleted.
You can find some information on how to create a list here:
Determine your list criteria
I would highly recommend you to please post this idea at our ideas forum (here).
Our product team, who monitors the forum regularly, can read your specific use case and understand why this would be a useful functionality or change. It also helps other customers facing the same issue to advocate for its implementation on your behalf by upvoting on the thread as well.
Kindly,
Pam