In a nutshell, there are two methods of submitting data to a URL: GET and POST. Our Integration submissions use POST, so if the script you're using to receive the data expects to receive data by the GET method, it won't work.
I think MemberWing is at least familiar with us, so if you're having problems getting their membership script to receive order data from us, I'd suggest contacting them to troubleshoot how you've got their script set up for your site.