If you do not wish for your users to have access to:

The sitemap of your site, or
The search tips option, or
You do not wish to display the textbox, or the standard GO submit button, do the following:

Login to your account and click on the 'Customization' tab, 'search box' option. From this screen you are presented with a list of search boxes available for your particular plan. Additionally, you are also presented with the capability to toggle on or off specific elements of your search box including the sitemap, search tips, textbox, and submit button.

Click to add or remove the checkmarks next to each item you wish to turn on or off as part of your search box. After making your choices, click the 'Continue' button to save your changes.

Your new settings will automatically appear on your search results, however, to keep your search box options / appearance consistent, you should copy and paste the new HTML code provided, in place of your current code.