DIAGNOSIS That's the protective lacquer coating over the stainless steel coming off. It's not the stainless itself. It's a cosmetic coating, but its failure is common.
FIX You need to remove all the loose coating to prevent it from flaking into food. Use a fine-grade Scotch-Brite pad and hot soapy water to gently scrub the entire interior lid surface. It will leave a dull, bare stainless steel finish. This is safe.
IF THAT DIDN'T WORK For stubborn patches, a paste of baking soda and water can help. Avoid harsh abrasives like steel wool, which can scratch the stainless.
HEADS UP The peeling is harmless stainless steel exposure, but the flakes themselves are a physical contaminant. Do not cook with a lid that is actively flaking. Remove all coating completely.