I think they could find your search terms from the referring url, but I am not sure how they are able to get their pages with your terms into the search results

I think they could find your search terms from the referring url, but I am not sure how they are able to get their pages with your terms into the search results and get the terms into their meta description. They must just have compiled huge lists of relatively specific search terms and have pages against each? But I would think this would be easy to identify and downrank.. It is a puzzle :/