If the partner site would allow you to add code to their thank you page, you could have them just add your existing Google Analytics tracking code to that page and then page views of thankyou.html would start showing up in your Google Analytics.
The problem with that though is that it will show ALL page views of thankyou.html, not just the page views that originate from referrals from your domain. So this would only work if you are sending traffic to a page on the partner's site that is exclusive to your domain.
You could actually set up a custom report in GA to show only page views of thankyou.html where the referrer is your domain, but you'd have a bunch of additional page views mixed in with your data that have nothing to do with your site.
