Looking at the form in question, it only accepts POST data. The only workaround I can see is to replicate the form on your own site, with the id code in a hidden field. Because most web browsers will notify the user that the form is going to another server, you should make this clear on your version of the form.

I should add, looking at that site in Firefox, I wouldn't enter my credit card information, it is horrible. The form elements overlap text, it is an awful design... as a customer, I wouldn't trust it. I think this could lose you conversions. On top of that, they definitely don't make it easy for you as an affiliate.

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The best way to learn anything, is to question everything.