The dnslookup section of the exim4 config contains
# ignore private rfc1918 and APIPA addresses
ignore_target_hosts = 0.0.0.0 : 127.0.0.0/8 : 192.168.0.0/16 :\
172.16.0.0/12 : 10.0.0.0/8 : 169.254.0.0/16
To allow one specific subnet thru change it:
# ignore private rfc1918 and APIPA addresses
ignore_target_hosts = !192.168.3.0/24 : 0.0.0.0 : 127.0.0.0/8 : 192.168.0.0/16 :\
172.16.0.0/12 : 10.0.0.0/8 : 169.254.0.0/16
Here it allows the 192.168.3.x network.