Yandex appears to load the favicons from their own cache. If your extension hits the sites themselves, you're leaking the fact that they are appearing in a person's search results to the target sites... and maybe even the query terms, via the referrer header. You should probably mention that fact to users who might not deduce it themselves.

My script takes the favicons from Google. http://www.google.com/s2/favicons?domain=news.ycombinator.co...