Why are there small white particles in the stainless steel mug cover? What is this?

Water alkali.

Hydrate or scale is mainly composed of calcium carbonate and magnesium hydroxide. Calcium and magnesium ions in water combine with bicarbonate ions to produce magnesium bicarbonate and calcium bicarbonate, which are unstable and eventually converted into magnesium hydroxide and calcium bicarbonate into calcium carbonate. Both of them are extremely stable, insoluble in water and are white precipitates.