The neck is rosewood, so it has natural pores in the grain. It's supposed to look like that. If you want a perfectly smooth neck, then you'd need to look at something like ebony for a dark fingerboard, or maple for a light one.

But rosewood fingerboards with small pores in the grain have made great guitars for a very long time. I have a 1965 Gibson acoustic guitar with a Brazilian rosewood board, supposedly the most sought-after rosewood for fingerboards and no longer commercially available. That has much deeper pores in the grain than that, yet it still feels fine to play. If it feels a bit rough under your fingers then a rub down with some fine grit sandpaper (P600 or P1000) should make it smoother.

I'm not sure what that stain is, but it might come out or become unnoticeable when you rub the board down with lemon oil as the board will darken in colour. Lemon oil is also a good fretboard cleaner. You could also try rubbing the stain with alcohol or turpentine - anything that may act as a solvent.