I've never tried using my touch screen but on my LG Envy Touch, if I flip the phone open and use the keypad I can click on items and drag them onto the pets While in CS Mobile. If they sit a little off from where they should be zooming in and making the image bigger gives me enough room to adjust things. I shall try clicking and dragging on the touch screen when the phone's done charging in a bit and let you know if it works.
edit: I just tried it. It works on my touch screen but is extremely frustrating and annoying. I managed to get a teal bracelet over onto the area the dog was in but when I tried to get it to go on her front leg all I managed to do was mess all of her other items up. So I'd think for some simple things it would work fine, but don't try to stack things or do anything too intricate. Unless you've got nerves of steel or the patience of a saint. Leave it for the laptop or big pc. D: