How to configure SMTP when using Windows Server 2003 as a mail server

This actually sounds more like the recipient domain's MX records are misconfigured. It's requiring authentication for sending to non-local e-mail addresses which they would normally require from their users who are trying to send a message outside the domain.

The MX records for the domain are pointing to particular servers to receive e-mail for the domain, but when you try to deliver to those servers, the servers are saying they are not responsible for receiving e-mail for that domain and thus require authentication in order to relay the message to the appropriate recipient.

Check to see which servers are responsible for the domain. If you are trying to send to alice@example.com, do the following at a Windows command prompt:

nslookup -type=mx example.com

You'll see a list of servers responsible for receiving mail for that domain. The list may contain the name of the provider that handles e-mail for that domain, say example.net. You may have luck messaging postmaster@example.net and tell them when you try to send to the domain you get the "requires authentication" response. Otherwise, you might need to lookup the whois records for example.net to determine the appropriate contact for the issue.

It might also help to contact the IT Managers for your partners to let them know about the problem and they may not be aware of the misconfiguration.

smtp.projectattack.com appears to land onto 67.215.65.132 whereas projectattack.com lands onto 109.109.248.82 and neither appears to answer on port TCP 25... You might want to verify your configuration(s) if the intent is to have your clients point to one of the hosts for their outgoing/sending SMTP relay.