Given that that seatpost may a few tenths of a millimeter too small for your frame (notice that the faces of the slot are much closer together at the top than at the bottom), any scratching that occurred would likely result from deformation of the seat lug from clamping onto the small-diameter post.

Plus, you should file the sides of the slot to eliminate the metal-to-metal contact above the binder bolt (and maybe below; hard to tell from the photo).

You might want to take the bike to a shop: they can measure the diameters of the seatpost and the inside of the seat tube and also (if necessary) ream the seat tube to eliminate burrs.