I leave it in the tank.
Cleaner shrimp, as with all other shrimp, will actually eat their old exoskeleton and gain some iodine from it.
I see this happen all the time in my girlfriend's 10 gallon tank. They don't eat it right away. They are rather secretive for a couple days after they molt (for safety reasons), so their new exoskeleton hardens. The one in the tank will chew and eat it.
Best,
Ilham