ipol-cart.user.js

// ==UserScript==
// @name         ipol-cart
// @namespace    http://tampermonkey.net/
// @version      0.1
// @description  add a cart to store IPOL images
// @author       kidanger
// @match        https://ipolcore.ipol.im/demo/clientApp/demo.html*
// @grant        none
// @require  https://gist.github.com/raw/2625891/waitForKeyElements.js
// ==/UserScript==

(function() {
    //'use strict';
    var css = document.createElement('style');
    var t = '\
   .gallery{position:relative;width:auto;height:200px}\
   .gallery .index{padding:0;margin:0;width:11em;list-style:none}\
   .gallery .index li{margin:0;padding:0}\
   .gallery .index a{display:block;background-color:#eee;border:1px solid #fff;text-decoration:none;width:13em;padding:5px}\
   .gallery .index a span{display:block;position:absolute;left:-9999px;top:0;padding-left:2em}\
   .gallery .index li:first-child a span{left:12em;z-index:99}\
   .gallery .index a:hover{ border: 1px solid #888888;}\
   .gallery .index a:hover span{left:12em;z-index:100}\
   .gallery .index a span img{ width: 150%; }';
    var tcss = document.createTextNode(t);
    css.appendChild(tcss);
    document.head.appendChild(css);

    var cart_div = null;

    function remove_img(img) {
        if (!localStorage.getItem('list')){
            window.localStorage.setItem('list', JSON.stringify([]));
        }
        var list = JSON.parse(localStorage.getItem('list'));
        while (list.indexOf(img) >= 0) {
            list.splice(list.indexOf(img), 1);
        }
        window.localStorage.setItem('list', JSON.stringify(list));
        console.log(list);
    }
    function add_img(img) {
        if (!localStorage.getItem('list')){
            window.localStorage.setItem('list', JSON.stringify([]));
        }
        var list = JSON.parse(localStorage.getItem('list'));
        list.push(img);
        window.localStorage.setItem('list', JSON.stringify(list));
        console.log(list);
    }

    function show_cart(div) {
        div.innerHTML = '';
        div.className = 'gallery';
        div.style = 'height:290px';
        var ul = document.createElement('ul');
        ul.className = 'index';

        var list = JSON.parse(localStorage.getItem('list'));
        for (var i in list) {
            var imgsrc = list[i];
            var li = document.createElement('li');
            var a = document.createElement('a');
            a.onclick = function(imgsrc) { return function() {
                console.log(imgsrc);
                remove_img(imgsrc);
                show_cart(div);
            }}(imgsrc);
            var t = document.createTextNode(imgsrc);
            a.appendChild(t);
            var span = document.createElement('span');
            var img = document.createElement('img');
            img.src = imgsrc;
            img.style = 'width:100%';
            span.appendChild(img);
            a.appendChild(span);
            li.appendChild(a);
            ul.appendChild(li);
        }

        div.appendChild(ul);
    }

    waitForKeyElements(".gallery-item-selector", function (item) {
        item = item[0];
        console.log(item);

        var a = document.createElement('a');
        var linkText = document.createTextNode(" add");
        a.appendChild(linkText);
        a.onclick = function() {
            var img = $('.gallery-0-blob-left')[0];
            add_img(img.src);
            if (cart_div !== null) {
                show_cart(cart_div);
            }
        };
        item.appendChild(a);

        var a2 = document.createElement('a');
        var linkText2 = document.createTextNode(" rm");
        a2.appendChild(linkText2);
        a2.onclick = function() {
            var img = $('.gallery-0-blob-left')[0];
            remove_img(img.src);
            if (cart_div !== null) {
                show_cart(cart_div);
            }
        };
        item.appendChild(a2);
    });

    waitForKeyElements('.result_0', function (item) {
        item = item[0];
        var a = document.createElement('a');
        var linkText = document.createTextNode("show cart");
        a.appendChild(linkText);
        a.onclick = function() {
            if (cart_div == null) {
                var d = document.createElement('div');
                cart_div = d;
                item.appendChild(d);
                show_cart(cart_div);
                a.innerHTML = 'hide cart';
            } else {
                item.removeChild(cart_div);
                cart_div = null;
                a.innerHTML = 'show cart';
            }
        };
        item.appendChild(a);
        console.log(item);
    });
})();

Instructions to install in the browser. (from @kidanger)

Install tampermonkey on chrome, on the gist click "raw" and it should propose to install the script.
On ipol, run a demo, and in the result gallery there should be "buttons" add and rm for each image. And a link "show cart" below the gallery. In the cart gallery, clicking on an image removed it (it does not uses the ipol gallery JavaScript unfortunately, their code is complex)