Search box widget displaying on page, not on layout

Search box shows up on page on the right hand side and cannot be deleted. This is only for the front page. User says it just appeared one day. It doesn't show up in the layout, and cannot be removed straight from the page. When adding the search box widget in through the layout, two appear (one unstyled):

This happened recently with another site too, with the search box appearing in the exact same place and not in the layout. But it went away after playing around in the All Sections and Sections layout–can't say exactly what I did to get rid of it before, but it was acting similarly to this case.
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