Cannot resolve "Error 553: relaying disallowed. Invalid domain" problem

Cannot resolve "Error 553: relaying disallowed. Invalid domain" problem

Recently we've switched to different hosting provider and cannot get Zoho mail to work. We can receive emails but cannot send, getting this type of message:

"Unable to send message. Reason: error 533 Relaying disallowed. Invalid domain - administrator@supersecretservice[dot]pl"

My research points to MX settings but they seem to be correct.
Domain: supersecretservice[dot]pl

Any help will be appreciated!

Regards
Paul