Here is a simple telnet SMTP test. Immediately when entering "RCPT TO" is denies relay access.
test@test01:~/Downloads$ telnet 10.xx.xx.xx 25
Trying 10.xx.xx.xx...
Connected to 10.xx.xx.xx.
Escape character is '^]'.
220 mx0.xx.xx ESMTP Postfix
EHLO mail.existinghostname.com
250-mx0.xx.xx
250-PIPELINING
250-SIZE 26214400
250-ETRN
250-STARTTLS
250-ENHANCEDSTATUSCODES
250-8BITMIME
250-DSN
250 SMTPUTF8
MAIL FROM:<my@email.address>
250 2.1.0 Ok
RCPT TO:<test@example.com>
554 5.7.1 <test@example.com>: Relay access denied
QUIT
221 2.0.0 Bye
Connection closed by foreign host.