Log into the control panel of the domain that has had its mail moved to Google Apps (or other offsite mail service). Under DNS Management for that domain, scroll all the way to the bottom of the page, and there click on Modify MX records. This will bring up another page for modifying the MX records. On that page, there is a checkbox near the bottom that says "Use this server to handle my email" (or similar wording). Uncheck that box, and click the save button.

Now when a email is sent from a Google apps account whose website is hosted on this server, it will not be rejected by the receiving domain.