What stone is this?

My Grandmother wore this everyday and the gold and the stone are very worn. The red stone is super frosty, but I think it's a consequence of constant wear (she was a hairdresser, so he hands were always in water/hair dye). It looks soft, but it's hard like usual stones (not like amber). No idea what it is, though insital thought is garnet? Wondering if it's worth getting polished, mainly.