In my opinion, the capacitor must be in GND, for me no sense to connect on output
The advantage of placing the cap on the second inverter output instead of GND is that it increases hysteresis, making a clear cut guarantee not to be so sensitive to the small schmitt region. It artificially enlarges the size, but, the input may now exceed VCC & GND slightly during the transition.
I guess there are different ways of wiring this circuit and will still function.