It depends on how deep are the scratches, and they do not look very deep at all!
The general value of precision ground stones as mentioned by
@davidpbest is unquestionable, but it misses Renzetti's point about what precision ground flat stones do. They are flat such that the pressure beneath them is so low they do
not remove much material, if any.
You can rub a flat stone even on a pristine gauge block, and not harm it, nor change it's dimension at all. The stone will knock down burrs and micron irregularities, and effect a "flat polishing" action that may leave all or nearly all the metal still there, but flatter, and more mirror-like. This action happens, even if the stone is as coarse as #300.
The scratches in your surface are not deep, and would rub away with abrasive paper if done in a series of grit sizes. You will not get this effect with precision ground flat stones. If you succeeded then then at least one of the (expensive) flat stones would end up no longer flat, but the nature of the flat stones is that even if you tried, you might wear yourself out only putting a better polish there without removing the scratches.
So - if nothing has to slide over the scratches, nor take a position that depends on that scratched surface, so that we are talking about visual appearance only, then start with #180 on a wood block, and take them out, blending the action over a larger area than the scratches. When they have just about disappeared, move to #240. If they have not gone at #320, back up to #240. Move to the next grade when you have ground out the marks of the previous grade. To match the final surface of the rest of the metal, it looks to be about #400 or #600 but you can choose where to stop.
The fact you will have "lowered the surface" to take out the scratches will not be visible just to look at, because you blended it over a larger area, and the actual depth change is miniscule. A scratch even only a tenth or two deep is still so very visible, and to carefully grind it away is not going to affect anything. A deep scratch like say 0.002" in a critical way surface is a very different matter.
My point is, you can fix this, but precision ground flat stones, though lovely to have, just won't work to remove scratches without ruining the stones, and I think, is not the way to go.