We have mail being returned from an Italian domain, but using gmail, it works fine. I've read where it can be our DNS problems, but not sure how a misconfigured DNS would affect a single outside domain.
Error.......#550 4.4.7 QUEUE.Expired; message expired ##
SMTP Extended Error 4.4.7 equates to:
4.x.x = Persistent Transient Failure
x.4.x = Network and Routing Status
x.x.7 = Delivery time expired
This correlates with the message you have reported with this error.
The most common cause for this error is that your message was held for an extended period of time at an intermediate relay server because that server could not connect to the 'next' server the message was to be delivered to. Typically this will be either an ISP's relay server which could not deliver to an end-user server, or a corporate edge server which could not deliver to a final mailbox store server.
In your case, it sounds like your senders mail server (or their ISP's relay mail server) is unable to connect to your mail server to deliver the message to you. I've seen this before where the sending mail server is behind an improperly configured firewall - specifically one configured to drop packets to / from bogons. It's difficult to be 100% certain if this is your issue without also seeing the Received: headers from the NDR, but this is one fairly likely scenario. Ask your message sender to check their firewall logs at the time they are trying to send a message to you to verify this.
Really not sure where to look internally.