We pull bounced emails or spam reports from our email service and will write this to the customer's last ticket as a private comment. If you have hidden comment emails turned on, you'll get an email message letting you know about the bounced customer email.
Steps we take for Deliverability
We take deliverability extremely seriously and any time there is a problem it's our top priority. So far we've had a stellar record in getting emails to the inbox and staying out of spam folders.
We have got our email domain certified, we employ the List-Unsubscribe headers, we are sure to send a valid html+text version and our templates use best-practices like valid image tags with alt messages. We use Sendgrid and their API for tracking spam requests and bounce/blocks, and we surface much of that right into your trouble tickets.
What you can do
If you have an old email list, and use it to send Marketr Blasts, there is a good chance you will send to a honeypot (trap email account) or get flagged as spam by your customers. It's a best practice to only send Marketing emails to pretty recent customers—people you've seen within a year, or have interacted via email in a short amount of time.