Hi,
If the e-mail clients (Thunderbird mainly and even Outlook) can send messages I presume SME server is working as it should.
If your 3rd party app (you don't say which one) cannot send messages... the problem it's on it.

Sorry to be so clear there are no intention to be rude.
If their tech support say it do not answer the query and you came here to ask support, you MUST supply us with information about what query was performed, what protocol was used, what version you are using and what's is the error message.
Just read your message again and try to think as someone who never saw your problem and you'll understand we have nothing to help you besides an info about your claim: "server is not answering the query and does not advertise what it wants"!!
Is your server updated?
Their software works with other linux or just with Microsoft ?
What configurations are used on that software?
It's trying to use authenticated connection?
What's the error message 3rd party software returns?
Have you tested to connect using telnet ?
If so, post your (or tech supp) attempt on any other server and on SME... so we can see what's going on!
If not... PLEASE test and report on two different servers (one SME , other one working!)
Thanks
Jáder