Your message couldn't be delivered because an email server outside Office 365 reported an error that it couldn't relay your message. It's likely that the email server isn't correctly set up to receive and relay messages from your domain. To fix this, forward this non-delivery report (NDR) message to your email admin.
For Email Admins The sender's message was routed to an email server outside Office 365 but that email server returned the error below. It's likely that the email server that reported error isn't set up correctly to receive and relay messages sent from the sender's domain. The server is not an Office 365 server - it will usually be one of your on-premises servers in a hybrid environment, a smart host email service that you're trying to route messages through, or possibly even an email hosting service you used in the past yet still have mail flow settings pointing to (e.g. your MX record at your domain registrar still points to your previous email service provider).
To fix this, check the server name to determine what domain, service, or server is reporting the error. The email server needs to be configured to either accept messages from anonymous users or to include the sending domain or sending IP address in its list of authenticated senders. On an Exchange server, you can set this up in the server's receive connector. If it's a smart host managed by another service or partner, contact the service or partner to configure their servers to accept and relay messages from your senders. Also, work with your domain registrar to make sure your MX records are properly configured.
Since the problem is likely due to misconfigured settings on an email server outside Office 365, unfortunately Office 365 support won't be able to help fix this issue.