That’s actually not a border, that blue color is the background that you added in your WordPress custom background settings.
You could use the “Slider Wide” if you want to use the full width space….make sure your image is large enough.
The .head-wrap (div around the header) has 40px of margin for the bottom. So you would need to remove that bottom margin and that would cover about half of that space. But you’ll need to only do this for the homepage, since that space is needed for all of your other pages. Add this code to do it –
.home .head-wrap {
margin: 0;
}