Enabling incoming email without your own email server

[espressomaker]

Our SharePoint site has incoming email enabled along with the prerequisite IIS SMTP service running and I believe all this is configured correctly. Problem is that our outgoing email server is not our own (and is not Exchange) and I'm trying to give the corp. email administrator some direction on what needs to be done to redirect the appropriate email back down to our SharePoint server. Essentially, the client is sending the email out to our outgoing email server but that server doesn't know anything about our SharePoint server. Incidentally, the outgoing email server is in a different DNS zone. TIA.