Extradium uses the server information configured in the SharePoint E-mail Outbound Settings to send emails to Extradium users.
However, Extradium lets you configure the email from which e-mails are sent from and will not use the generic, unique e-mail address used to send SharePoint alerts or group assignment notifications. By default, the sender e-mail address is a fake e-mail address ending with "@company.com".
There are typically two reasons why external users might not receive Extradium-specific e-mails:
1. Your SMTP Relay does not accept e-mails sent by an "unknown" domain, such as "@company.com". In this situation, the solution is to update the email templates stored in the Extradium E-mail Templates lists that are used by Extradium. For e-mail notifications you want to send from the Extradium Central Administration Site, you will want to update the Sender Email property of the Extradium E-mail Templates list located in that site, the url of which typically is [CentralAdminUrl]/
Extradium uses the same mechanism of connection and relaying emails as the SharePoint product from Microsoft.
If you are unable to send emails from Extradium please check if you outgoing emails are working from SharePoint like Alerts for a list.
If that does not help then the reason could be related to SMTP service permissions. In most cases SP is deployed within an organisation and SMTP relay within internal users is allowed from the SP servers. With Extradium in picture the scenarios differs a bit since Extradium is using the same SMTP service however this time it is trying to relay email to outside users (outside of your domain - in majority of cases). Please work with your email system administrator and make sure SP servers have the permissions to send email to outside email addresses outside of the internal domain users.
Best way to troubleshoot this is to try to send an email via telnet and see the end result. You will get the exact error code with 550 message for the reason of unable to relay.
Instructions on how to send email via telnet can be found on this blog: http://www.spamsoap.com/how-to-manually-send-an-email-message-via-telnet-to-port-25/