JSFiddle - React, Tailwind, and code Playground

HTML

<div class="icon"></div>

CSS

.icon {
    height: 200px;
    width: 200px;
    background-image:url(http://i56.servimg.com/u/f56/12/05/75/97/e410.png);
}

JavaScript

var icons = document.querySelectorAll('.icon');
var imagem = 'url(http://i56.servimg.com/u/f56/12/05/75/97/e410.png)';
for (var i = 0; i < icons.length; i++) {
    var este = window.getComputedStyle(icons[i]).backgroundImage;
    if (este == imagem) {
        // fazer algo
        console.log('Tem imagem!');
    }
}

/*

if( $('.icon').css('background-image') === 'url(http://i56.servimg.com/u/f56/12/05/75/97/e410.png)' ){
    //do something
}
*/