When a user clicks "I'm not interested" on a request, it means they don't have an opinion on that particular request and simply don't want to see it again.
Clicking the button will clear the request from a user's dashboard so it doesn't come up every time they log in.
It does not add a negative weight to the request when it comes to your reports. Requests can only be influenced up rather than down.
Users can find their old "Not interested" requests by clicking "Requests you want" and selecting "See your previous choices":
On this page, if you click "I'm not interested" again, the Snooze function is disabled and the request will start showing up on your Dashboard again.