5.7.1 = Delivery not authorized, message refused
Looks like blacklisting or reverse DNS checking.
I would look into your SMTP relay log to see at which step it is refused.
Reasons I can think of are :
The user adress is blacklisted
your domain is blacklisted
you don’t give the FQDN during the EHLO command.
you don’t have a reverse DNS entries on your MX record.
on the other hand : the first code 553 is normally “too many recipients”.
So that could be they customized the response code and that they are meaningless …
i have had experiencing this problem, but it has been solve by enabling the FQDN on my E-mail server.(i am using M-Daemon e-mail server ver 9.6.4).
the option command is located at Miscellaneous Options, put tick / enabled on this command below:
Use FQDN Value in “by” section in all “Received” Header stamps.
once it’s enabled , it works fine. my mails have been delivered without any problem.
if you’re just an e-mail client user, please get your network administrator to do it.