Support for touch devices in drag and drop, image target

There are some neat little JS libraries that could probably help with this.

I actually had success integrating this one: https://github.com/furf/jquery-ui-touch-punch

Just add the script to your theme's .info file and then initialize it on the group member selector:

scripts[] = js/jquery.ui.touch-punch.min.js

$('.quiz-grouping-member').draggable();