Not sure. The metal outer cover could be merely polished, with no weight increment. And a mirror reflecting only 95% of the falling light [i.e. rather lousy mirror] would be absorbing 16 times less energy than a "neutral grey" object. A better quality mirror would necessitate even higher laser beam power levels.
Depends quite a bit on the wavelength of the laser beam. Not to mention, these things are mega-watt range. I doubt you could get anything through the atmosphere without picking up something. I work with industrial lasers every day, a fleck of dust on a lens is enough to cause a burn spot and wreck the lens. Scale that up to Mega-watt ranges and even water condensate on the surface of the missile has probably enough absorbtion to make the polish unimportant. We're talking about beam spots several feet across with mega-watts of energy. I know the mirrors in the lasers I deal with are Molbdnenum, tough as hell, but I suspect way too heavy and impossible to clad a missile with it. Anything else and the laser is just going to burn through it.
I suspect this has been taken into account by these guys, which is why it's SO powerful. Even if only a few percent gets absorbed, it's prolly way more that it would need.