LogScale can be configured to use Postmark instead of using SMTP. To do this, you'll have to sign up for Postmark and create a new server. When you do, make sure that the email address from which LogScale will be sending mail has been verified in Postmark. See their documentation on Verifying a Domain.
You'll also have to get a security token from Postmark. When you do, add that to LogScale's configuration file with two entries like these:
You would adjust the values here for your server's token and domain name. See the Postmark documentation page for more information on integrating Postmark with LogScale.