Assume we have a neutron star that has cooled down so far that it no longer emits visible light. If we illuminate it with a powerful external light source, what would it look like? Would it reflect light, would it scatter it, would it re-emit it with a different wavelength, or would it remain completely black?
Neutron stars are very smooth. According to Wikipedia, their maximum surface irregularities are on the orders of millimeters or less. As a neutron star cools and its luminosity decreases, most likely it would exhibit specular reflection because of its thinness. Diffuse reflection, or the scattering of light by objects, is caused by microscopic bumps on the surface, scattering the light. In this case, the surface would be smooth, so most likely the surface would cleanly reflect light. If the neutron star is completely cold, it wouldn't emit any light, but if you shone a light on it, it would reflect it back. For more information on how neutron stars cool, check out this astronomy SE post: What happens over time as a neutron star cools?. It shows that it would take more than a billion years for a neutron star to cool down.