Notes
How to fix Unrouteable address for a local domain with Gmail smarthost
Add your domain name and corresponding smtp server to the list of hubbed hosts
# echo 'themactep.com: smtp.gmail.com' >> /etc/exim4/hubbed_hosts
then change hubbed transport to smarthost to have SMTP AUTH
# sed -i 's/transport = remote_smtp/transport = remote_smtp_smarthost/' \
/etc/exim4/conf.d/router/150_exim4-config_hubbed_hosts
(from Exim mail list)