Oven pilot making high pitched noise (when off)
I had the same situation a number of years ago with the pilot on a gas furnace. Since the furnace was next to a bedroom it was very irritating at night.
The solution: The gas pressure to the pilot needs to be reduced slightly. Locate the gas shutoff valve for the stove. Lower the pressure of the gas to the pilot by slightly closing the valve. You shouldn't have to turn it very much. I'm betting that will solve your problem.