Here is a quick hack which doesn't require any plugin installation, instead you just need to add a few lines to your current layout's CSS file. Works perfectly for me in v4.2.2

Navigate to <ECLIPSE_HOME>/plugins/org.eclipse.platform_<VERSION>/css then open up the CSS file of whichever layout you are using, e.g. mine was e4_default.css. Now append the following snippet to the file:

#SearchField {

   visibility:hidden;

}

Now just restart Eclipse and the box is gone.

*Edit

It appears that the layout file e4_basestyle.css is used universally, regardless of your current layout. Thus you should be able to add the above snippet to that file and this fix will be persistent, even if you change layouts.