Back in 2009 I posted that automated tools like those at mxtoolbox will return false negative results on the SMTP banner tests. (http://semb.ee/banner2007)
This is because the SMTP banner presented for inbound email is different to outbound email.
This is still the case with Exchange 2010 and 2013. You shouldn't try and change the Receive Connector configuration to "fix" this problem as will cause further issues with Exchange.
However with those tools providing false information, it raises the question of how do you easily test the banner so that you can see how a remote server will see your server?
Of course one way is to simply send an email to a remote server which you have control over, and check the headers. That isn't always practical and if you don't have your own server, using something Gmail or Hotmail might mean the message gets block because you haven't configured things correctly.
One of the blacklist operators has setup a system that will show you exactly what you are sending back, in the form of an NDR.
The details are here:
After sending the message, you will get an NDR back similar to this:
helocheck.abuseat.org rejected your message to the following e-mail addresses:
helocheck.abuseat.org gave this error:
*** The HELO for IP address 126.96.36.199 was 'mail.example.co.uk' (valid syntax) ***
A problem occurred during the delivery of this message to this e-mail address. Try sending this message again. If the problem continues, please contact your helpdesk.
Diagnostic information for administrators:
Generating server: server.example.co.uk
helocheck.abuseat.org #550 *** The HELO for IP address 188.8.131.52 was 'mail.example.co.uk' (valid syntax) *** ##
Original message headers:
This service is a quick and easy way to verify the server is configured correctly.