Zimbra's MTA is Postfix, so if you are comfortable configuring Postfix in general you are just one step away from doing so in Zimbra.
On each Zimbra restart, Zimbra rewrites the Postfix and Amavis configs based on stored values in the Zimbra server's local configuration.
Except that not every value is stored that way. :-)
So, at the risk of oversimplifying, to get you started here's what I would suggest:
First, get comfortable with the zmlocalconfig command as it is used to edit a number of Postfix variables in main.cf. So, for example...
...will change what Postfix spits back in response to a HELO (note the escaped dollar sign).
zmlocalconfig -e postfix_smtpd_banner="\$myhostname NO UCE ESMTP"
Second, poke around in /opt/zimbra/conf and look for *.in files. On service restarts, Zimbra uses e.g. /opt/zimbra/conf/amavisd.conf.in to rewrite /opt/zimbra/conf/amavisd.conf prior to launching amavis.
Most everything used to be in the *.in files, but those get overwritten when doing a Zimbra upgrade, so Zimbra has been putting more and more into localconfig to reduce the administrative tasks required to complete an upgrade.
Hope that helps get you started,