The way to remove scratches is to make more scratches... with an appropriately coarse piece of sandpaper. Once the original scratches blend in with your new scratches, move to a slightly less coarse grit of sandpaper and keep sanding. Gradually work your way to finer and finer grits until the surface of the blade is almost completely smooth looking again. Then polish it with flitz metal polish or a similar product to finish it off.
There are youtube videos that go through this process, and that's where I learned it from. I like to wear nitrile gloves when using flitz, but I guess it's not really necessary because it is supposed to be non toxic.
You may be tempted to just focus your sanding on one area of the blade, but this is a bad idea. You need to sand the whole surface so it's even. If you only sand in one spot then you'll end up with an uneven dip in the surface of the metal.
Once you're done, you'll probably need to resharpen the knife.