I'm seeing two areas of damage in all of your photos. Do you mean the gray/worse looking one? Or are you concerned about BOTH stain areas?

If this is a solid hardwood, then a sand and refinish will work - but that requires then entire floor to be dealt with. It is *possible* to get a little bit of finish applied to this but it will always look different until it is fully dealt with (sanded past the stain and refinished).

If this is an engineered hardwood with a significant wear layer, then the same applies as above...or you can pay a professional to cut out the damaged planks (I would deal with both stains...and please take the plant else where) and drop in new ones. New ones would come from your EXTRA box of material you kept in a safe place for just this type of emergency. If you don't have an extra box, you are probably out of luck for a plank removal/repair option.

If this is engineered hardwood that CANNOT be refinished, then the only option = remove and replace the planks (again...from extra planks kept for just this eventuality).

If this is bamboo, see all of the above options....it will depend on type of bamboo, etc.

I see 7 planks that require damage control (counting both stains). If you have the planks, it should cost you a few hours of a hardwood flooring professionals time to deal with this. I would guess 3-4 hours of work. Should be $300 - $600 to get it done...depending on where you live. I've seen local installers charge $80/plank to do this. You have 7 planks. It depends on if they bill this as a "minimum charge + labor" or if they charge by the plank.

Let us know what type of floor this is and if you have replacement planks (you will need 7 of them).