service.arpa has no MX records.
Question and response
Question
dig service.arpa. MX
Answer
The response has no answer records.
Authority
service.arpa. 604800 SOA prisoner.iana.org. hostmaster.root-servers.org. 1 604800 60 604800 604800
Additional
. 0 OPT ; payload 1232, xrcode 0, version 0, flags 0