Since this error is happening on a server that's outside Office 365, you'll need to check a few things to fix the problem. ...

Since this error is happening on a server that's outside Office 365, you'll need to check a few things to fix the problem.

Check the NDR for information about where the problem is happening. For example, look for a domain name like contoso.com. The recipient's email server could be causing the problem, or it could be due to a third-party service that's filtering the messages.
Work with the owner of the server to set it up to relay messages from the sending domain. 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.
Work with your domain registrar to make sure your MX records are properly configured.

Unfortunately, since the problem is due to misconfigured settings on an email server outside Office 365, Office 365 support won't be able to help fix this issue