Google Outbound Services Configuration Guide - Manual (Page 33)

Microsoft Exchange 2007/2010 (Private DNS Method) 35
9. Click OK, then click Next to continue.
10. Click New, then click Finish on the Completion page.
Method One: Apply Anonymous user access to the
connector
The first method to allow reinjection is to set the receive connector to allow
Anonymous Users. This is recommended for most configurations.
The first step in this process is to add the Anonymous Permissions Group to the
connector.