@elise1 - If all the contact owners already have their inboxes connected to HubSpot then the data (x contact replied to y email) should populate on the email reporting pages showing reply rates & which contacts replied to what email. Additionally, the data will show up in workflows & lists to build with.
What will not show up with your current configurations is the actual content of the reply that lands in the contact owner’s inbox. Aka logging the email in the CRM. To get that functionality the inbox needs to be setup as a team inbox.