We'll definitely think about how to improve this!
We added the Feedback button in the Menu options so that people used the Feedback page: https://duckduckgo.com/feedback
That way, the reports are really actionable (since it's broken out by type) and people don't spam the form :\
I saw that link, and the categorization seems fine, but following the feedback link doesn't automatically capture the search data. You need a link that automatically includes the search query, so that the user doesn't have to manually transcribe that data.
Ideally, you should do so via JavaScript inline on the search query page, to make it easy for the user to note the bad search results without switching back and forth between the results page and the feedback page.
Click feedback link, click category, identify relevant/irrelevant results, optionally type a sentence or two, submit. That flow needs some UX optimization.