Unfortunately, we do not support replying through email yet but we do have it in our backlog.
When we implement the feature, we'll do it through an integration with SendGrid and/or MailGun. You'll set your inbound email domain in those 3rd party services and enter the credentials in Tribe App.
Another approach would be just providing a way for our customers to define the reply to address, and let them use Tribe API and any 3rd party service such as SendGrid to receive the email and take the desired action using the API. This will be helpful if you want to create a new post based on each email for instance, but won't work for replying to a post through email. It's worth mentioning implementing a custom reply to address needs way less effort comparing to the first solution.
Let's discuss in comments.