That seems to be a malformed HTML output, but unfortunately that code is not printed nor related to this plugin. It looks like the default search form is printed to the document body tag.
Try checking the theme search.php or the searchform.php files for unclused HTML tags or incorrectly printed get_search_form() function.
The theme may had a hidden search or a search trigger on that location and the automatic replacement may forced it to display somehow, that could explain the issue for sure.