The record of search history which appears in the search box on Yahoo!Xtra is actually a feature controlled by your browser, not Yahoo!Xtra.
If you have Internet Explorer as your browser, you can stop the search history from being generated by following the instructions below:
On the AutoComplete Settings window you can click the "Clear Forms" box to delete your current history, or you can uncheck the "Forms" box to permanently stop the generation of the search history.