Sometimes you're left with stuck on bits like that the lye won't take off because they are pure carbon, no grease left in them for the lye to work on. Electrolysis can usually loosen them up, or you can expend an inordinate amount of elbow grease working them off with a stainless steel scrubber or wire brush. If you have a steady hand, you can also use a 1" putty knife, working slowly and always keeping the leading edge of the blade flat against the surface of the pan so as not to leave scratches. This works well on the outside, but those inside round corners on skillets can be tricky; sometimes you just leave what you can't safely get off, and let it blend over time with the new seasoning.
If you're still left with black stains after you get these removed, try spraying full strength white vinegar on them, wait a couple minutes, and scrub with steel wool. Dripping vinegar will make some streaks; just even them out by scrubbing the entire pan with the steel wool.