Hi, Karen. You should be able to get the black stains out. This is actually mildew. Just like with any mildew, the first choice is household bleach like Clorox. Put this on with a sponge mixed half and half with water while wearing rubber gloves and eye protection. Try to put on just enough to work but not so much that you flood the floor. Then neutralize the bleach with 1 cup of white vinegar to a gallon of water and again try to limit how much water you put on. Finally, rinse with clear water.
After this is dry, see if any of the black is left. If there is a significant amount, you might try the same process again except using oxalic acid in place of the bleach and neutralize with 1 cup of bleach to a gallon of water. This might turn the floor a little bit of a pinkish color, particularly with oak. You can get oxalic acid in the paint department of home centers under the name Wood Bleach. Wear gloves and eye protection while using it and a dust mask while mixing it.
You will have to resand any areas of the floor where you used anything mixed with water but it will just take a light sanding, not a lot of wood removal with a big, heavy sander. Use the same grit paper as they used on the last pass when they sanded your floor or the grit that they used when they screened it and you can do this with a finishing sander or even by hand. Be sure that the wood is dry when you sand.