Are your emails getting bounced from SMTP servers out on the Internet.
Check if you are issuing outbound SMTP sessions by using the local server FQDN, and not the server name used in MX/SPF records.
Change the FQDN in the properties of the Send Connector.
You also need to change the permissions assigned to the Anonymous Logon by using the following EMS command, if your Mailbox and HT servers are on the same box:
Get-SendConnector “NameOfSendConnector” | Remove-ADPermission -User “NT AUTHORITYANONYMOUS LOGON” -ExtendedRights “Ms-Exch-Send-Headers-Routing”