You might consider configuring exim to exclude original message from bounce in order to reduce chances to get blacklisted by other mail servers. As they might think that you are spamming them.
Here a guide on how to achieve the desired on a server with Directadmin and Custombuild 2.x. You need to have exim.conf from 4.x branch.
Open in an editor (create if missing) /etc/exim.variables.conf.custom and add the one of following 2 lines into the file:
bounce_return_message = false
If bounce_return_message is set to false, none of the original message is included in bounce messages generated by Exim.
bounce_return_body = false
If bounce_return_body is false, only the message header is included.
Save the file and exit the editor.
Make sure to create backups of files matching the /etc/exim* as they will be overwritten if you follow the guide further.
IMPORTANT! DO NOT run the following commands if you have a customized exim configuration, as you will loose all the customization. Contact your system administrator or us if you're unsure.
cd /usr/local/directadmin/custombuild/ ./build update ./build set eximconf yes ./build eximconf
More reading: http://www.exim.org/exim-html-current/doc/html/spec_html/ch-main_configuration.html