AdminCP > Templates > Your theme's templates > header Templates > header > and search for;
<li><a href="{$mybb->settings['bburl']}/downloads.php"><img src="{$theme['imgdir']}/paperclip.gif" alt="" title="" />Downloads</a></li>
and Delete the following code from it;
<img src="{$theme['imgdir']}/paperclip.gif" alt="" title="" />