My expensive multicoated filter has oil or grease on it, but it is brand new. What happened?
If what you are seeing is the multicolored sheen typical of oil, it is most probably not oil or grease. The multiple layers of very thin coatings used on multicoated filters show birefringence that looks similar to oil sheen. Vigorously rubbing the surface to remove the sheen only worsens it, as the first coating surface is made uneven.