How can I get rid of the box outline surrounding the Menu Bar?

To remove the grey box outline that is surrounding the Menu Bar, you can add the following code to the style.css file:

.navbar .navbar-inner, #under-navigation {
  border: none;
}
.dw_top_15_hide.desktop .wrap-navigation, .navbar {
  border: none;
}

Note: If you still face there issue, you can send me your site for further checking.
Hope this helps !