Scratches can't really be removed without heavy industrial equipment to recoat the lens. If you've ever ground a lens before (and don't start with a camera lens!) you probably have the tools to regrind the front element but that will result in it being uncoated and probably flaring worse than with the cleaning marks.
In the early 70s the Nikon School came to my town and I "enrolled". I remember the man saying that Nikon would mix and match elements, some under-spec and some over-spec such that the entire group would perform as desired. If you damaged the front element Nikon could replace it but would have to grind an element to match the damaged one's specific curvature. Very expensive, but Nikon did offer the service.
This was probably just a shill to boost sales of Nikon's filters, which were a good bit more expensive than the competition's, but I took it to heart and *always* kept an L37c on the front of the four lenses I owned at the time. Eventually some of those lenses looked terrible but the glass was still perfect, (unlike most of my pictures).
There are people who clean their lenses at the first sign of dust. They usually do more harm than good. I like the car commercial where the next owner is telling the original owner how to care for "his" car.
A rock pile ceases to be a rock pile the moment a single man contemplates it, bearing within him the image of a cathedral.
I once had a Componon-S 240mm in which the prior owner cleaned the front and rear surface with a Brillo pad. I came across another with excellent glass and a beat up, slightly different body. So, I swapped out the good glass and put the scratched pieces in the beat up barrel.