You should check Zimbra's trusted network setting.
If it includes your firewall/gateways internal network address you have configured it to be an open relay.

Congratulations.
If your local area network is in LAN and your network is something like...
192.168.0.x or 10.x.x.x then you should definitely NOT include your firewall address in the trusted network.
For some obscure reason Zimbra's default configuration is very SPAM friendly when it comes to local area networks (LAN).


Easiest way to fix this is simply put an /32 at the end of the LAN address in trusted network setting. This will make the Zimbra server only trust it self. (And those who log in to it with proper credentials.)