Short answer
HubSpot's KB: influenced contacts are new and existing contacts who engaged with a campaign's assets. Once a contact is marked Influenced, it cannot be removed. Detail tabs only show for campaigns created after April 1, 2022.
1. In HubSpot
The relevant screen in my demo portal.

2. Worth knowing
Add assets to the right campaign before launch, since influence stays.
3. Related
Adding assets and zero-session campaigns.