I believe it's to do with the HTML input search type
This isn't documented anywhere that I know of nor is it in the spec, but you if you add a resultsparameter on the input, WebKit will apply a little magnifying glass with a dropdown arrow showing previous results. (Thanks to Mike Taylor)
This is an old thread but I have a similar question -
On this page: http://www.groundtradesxchange.com/xf/index.php you can see that the search magnifying glass is out of vertical alignment with the search box. I don't care if that icon goes away or gets aligned, but I'd like it to be cleaner than what it is now.
It got out of alignment when I reduced the height of the dark brown nav bar, but the search bar remained in it's location relative to the bottom of the div (putting the search bar at the top of the now-smaller nav bar). In #QuickSearch I changed top: -52px to top: -40px and everything moved nicely to be aligned vertically, except for that icon.
I looked through all of the images and icons for the style and couldn't find that image in any folders, so I'm thinking the issue is similar to the html5 one mentioned above, however, removing 'type="search"' from the template search_bar doesn't remove the icon.