If the website attempted to deliver to SmarterMail it would first have to make an SMTP connection, which is where you would look first. (Pro-tip: Make sure that your SMTP Server Log Level is set to "Detailed").
If there are no attempts to connect and deliver the email in your SmarterMail SMTP Logs then it is a problem with your WordPress/PHP/Webserver and you will have to refer to your php_mail.log and php_error.log for clues (we always use the WP-Mail-SMTP Plugin
https://wordpress.org/plugins/wp-mail-smtp/ for all of our hosted WordPress sites and use SMTP Authentication instead of the default PHP mail() function as it is easier to track down issues, and eliminates the need for SMTP Authentication Bypass).
If the email from your WordPress site shows in in the detailed SMTP Logs but still wasn't received it is only then when you would check the SmarterMail Delivery Logs for an explanation.