I don't believe that anyone was proposing equipping the attacking missiles with (flat) mirrors which would bounce the beam directly back to the airplane from which the laser was shot.
I think that, instead, the proposal was simply to coat the outside of the missile with the same reflective substance as is used on the mirrors of the laser so that any incoming beam would be bounced away and thus rendered harmless.
A flat mirror would, of course, be aerodynamically problematic, but simply "dipping" the outside of the missile in silvery stuff would reduce its absorption of light and thus would reduce its vulnerability to laser beams.
As it turns out, a mirrored surface is no protection against a high-energy laser. It has been demonstrated in lab tests that the energy transfer is enough to destroy a target.
I suppose you could “spin” the missile as well as reflective coating the skin, so that no single targeted spot gets overheated. I really don’t know the physics of these particular lasers well enough to know if that would work.