I certainly hope I'm wrong but do not think you are going to be able to do an easy fix in this area, just to deep and grain is cut.
I often use the steam process and have more success with bare wood. Never on a scratch like this but on dents. Try the previous suggestions as do not think you can do any harm. I don't know your project or the condition of the rest of the stock and perhaps it's something you can live with. I certainly wish you much success. In hind-sight, on screws like this, I always protect the wood with masking or electrical tape.
Be Safe !!!