Tree crickets shed their outer 'skins', or exoskeletons, six times between the nymph stage and full adulthood. Their lifecycle consists of: nymph, 1st instar, 2d instar, 3d instar, 4th instar, 5th instar and adult. As they grow and develop, their outer 'shell' does not -- thus the need to shed. Within minutes, they eat the entire exoskeleton - which once it is shed is referred to as the exuvium/exuvia/exuviae.
Female Oecanthus varicornis completing a final molt. Note the coloration on the exuvia.
Below is the beginning of the molting process for a Black-horned tree cricket. Generally, the tree cricket will cling to a leaf with their hind leg 'claws' and hang upside down. With this assistance from gravity, the exoskeleton splits and the tree cricket slowly emerges from its old anchored shell.
This is a Narrow-winged tree cricket undergoing a molt.
Here is a Two-spotted tree cricket freeing itself from its exoskeleton.