Here is a quick hack for making a whitelist of destination domains for your exim smarthost configuration. It means that emails will be sent only to domains which you explicitly specify.

You may ask why “hack”? Because Exim will send bounce emails which most probably is not what you want, reject could be a better behavior.

Find your Exim configuration file for smarthost, /etc/exim4/exim4.conf.template under Ubuntu. And edit domains configuration parameter specifying colon separated list of allowed destination domains as a value.

domains = domain1.com:domain2.com

If your use Ubuntu update main configuration file by executing update-exim4.conf from command line as root user.