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What's the tool that's in the styrofoam cut-out above the battery? Is it some kind of lifting tool? Mine is missing, even though I've never taken it out and bought the car new! Thanks.
As mentioned, the recess is to store the GM tow hook. Other companies make similar but prettier versions of the hook, some of them are just for appearance.
Since your car is a Z06, it probably has a receiver at the front and rear to thread in the hook. Be careful, the threads may be dirty or slopped with paint and the shaft may go in at a slight angle. Getting to the rear receiver requires removing a small cover door on the back.
I bought the GM hook and store it in the recess. Since I have it, I'll never need it.