How to remove white border from blur background image

The simplest way to do it is by adding transform: scale(1.1).
Try it here.

#overlay {
 position: fixed;
 left: 22.5em;
 top: 3em;
 height: 75%;
 width: 50%;
 background: url("https://s-media-cacheak0.pinimg.com/originals/ae/b4/c5/aeb4c53cab2b550187644af503a0f17e.png");
 background-size: cover;
 filter: blur(9px);
 transform: scale(1.1); 
}