The border is actually a white background which shows up because of the way the image is positioned when the browser is resized. We can fix it by adding background-size: cover; to the hf-bg on line 1329 in your css like this –
.hf-bg {
background: url(http://rcs.nextdev.co.uk/wp-content/uploads/2014/02/couple-talking.jpg) center no-repeat;
background-size: cover;
}