This is the saliva-like remains that are left on a thumb by a thumb sucker. Usually builds up after an all day or night session of thumb sucking. It stinks, it's odorous and disgusting when they touch you with the thumb they sucked from. Thumb juice has a consistency much like saliva but thicker. Thumb suckers also tend to smell the juice off of their thumb when they pull it out. In return causing them to suck their thumb again and creating more thumb juice.
Ewww Matthew, don't touch me with your hands that have that disgusting thumb juice on them.
Hey thumb juice! Stop sucking your thumb. It's nasty!
Chica, Chica, thumb juice!