So, then require a person to be logged in to complete the feedback. Or create a course, add all students to it and place the feedback there. However, I believe that you will not get as accurate a view if students have to log in because then they know their answers are tracked and traceable.
The other thing you could do, is password protect the feedback and only give out the password to students within their courses. This way you could actually give out a separate code for each course so you could verify that way.
I do this to stop Tom, Dick and Harry randomly coming to my site and filling out feedback. My first question is password and then the second page is conditional on them typing the correct password in.