Get a 3M green color scotch brite pad. Make sure to remove the band or the links in question and clean them with soap and water. Trim a small square section of the 3M pad just about the width of the band and lightly brush the area in the same direction as the brush marks that are on the band. Make sure to keep the pad straight in the direction of the brush marks. Always use even pressure and try not to brush too hard unless the scratches are deep. Brush the scratched area of the band until the desired finish is achieved.
I've done this with several of my stainless steel watches including my 42mm Apple watch with link band and if done correctly you will never have known the band was scratched.