I've connected my Hubspot to my gmail account. But it's pull "all" emails into Hubspot which is not useful to me. For tracking email in Hubspot, I only want that for the contacts I have in Hubspot. Can that be done?
In this case, the behavior you're experiencing is expected behavior. If you would not want to log all emails, you can either disconnect your inbox or connect a different inbox to that channel and connect your inbox as a personal inbox so you can track and log the email you would like to see in your account.
With a shared inbox ( how is connected currently) is used for a team email channel, your team can view, manage, and reply to emails in the conversations inbox. A team email address is an email address that multiple users have access to and use to communicate with contacts.
And all incoming emails sent to a team email will be visible to your entire team, so do not connect an email account that you use to send personal emails.
If a visitor sends an email to the conversations inbox using an email address that is not already associated with a contact record in your account, HubSpot will automatically create a new contact record for that email.