If you only have that URL at one third party location and you wouldn't mind changing your other links, then I'd suggest
setting up a URL forwarder for the current URL that you have with the third party, updating the form to have the hidden field that will be captured by the new URL, and also use new URLs for any ways that you're pushing people to the page.
Without doing this, you won't really have any way to differentiate your traffic from the evite traffic.