If your email-to-SMS request is successful, with no erros or problems, you will not get any response by email (unless you're using the SandBox service). However, if there are any problems with the format of your email, or problems sending to any of the numbers you specify int the email, you will get a verbose email response with details of the problem(s) encountered.
You will not get any response if your API username and password (included in the email subject) were incorrect, or did not contain the '%' character to separate them.
To use the Messagebox's Stop Group and make sure that no numbers are included in it receive any message, please call Text Marketer and make the request.
If you don't know your API username and password, you'll find them when you log on to the Text Marketer web interface here:
https://messagebox.textmarketer.co.uk/(Account Settings > API Settings)