My blondi will full out attack my tongs when I fish her exuvium out. She's normally very laid back. Then, there's my Tigerrump. Molted before I sent it off to its new home. Little thing eats its exuvium, and gets VERY upset, if I take the skin.
Mine seem to concentrate mostly on the abdominal portions of the molt. I think what they're doing is "sucking" on the molt to recover whatever fluid is left; just an economic strategy. The disadvantage for me is that they munch up the molt enough to make sexing it more difficult.