If you try to polish the paint to remove some of it, it will come off quickly, as the polishing compound is very effective on paint only. So if you just want to remove say, the edges of the paint repair where it extends beyond the scratch, you need to do this very carefully.
We recommend wrapping the polish cloth around a wooden block to get a sharper edge to polish with. Use the edge of the block to more precisely control where you apply the polish. This, combined with careful pressure, should allow you to get those paint margins removed while leaving the new paint in the scratch.