external address sending mail thru server, maybe

This is an Exchange  2007 question, so if it needs to go somewhere else, let me know.

I found evidence on my Exchange 2007 sp3 server that an external address is trying to send email thru my server. We are not an open relay.

The troubling thing is that my mail server is not stopping the messages from getting to our SMTP relay. 

The only thing that has stopped delivery is the recipient email systems not accepting the messages.

Where do I start to look for the source of this problem?

Thanks