There are a few things that you can try. This looks like water damage or some sort of a product was dropped on the top of the table that caused this damage. Did you happen to use a hand sanitizer and set the bottle on the tabletop? Could this be fingernail polish remover or could it be some water that was left on top of the table? You see it really makes a difference what was spilled on the top of the table. I can give you some general things to try to get rid of the damage.
In a small bowl mix equal parts of vinegar and olive oil together. Now take a cloth and apply it to the stain on your table. Start rubbing this in and follow the grain of the tabletop. The vinegar will act as a stain remover while the olive oil will act as a polish.
You can try to lay down a clean cloth over the top of the stain and use your iron to iron over the cloth. If this is water damage it can lift up the water and restore the tabletop. However, if this is anything else it will not work so good.
The last trick that can work is to use toothpaste. You will put a little of this on a clean cloth and rub this into the stain on the table. You keep rubbing until the stain has been removed.
Keep in mind if this was fingernail polish remover or anything that has an alcohol base you may need to refinish the tabletop.
I do not know what type of finish is on your table top so please be careful and only try a small inconspicuous area before doing anything to the top of your table. Maybe a spot underneath just to see if the 'remedy' leaves any lasting 'stains' as black finish sometimes reacts different than just regular wood stains.
I have used a hairdryer on some spots and it worked but you have to be careful and only use it on low setting. Also, do not hold it in one area but keep the low heat moving around the area and do not let it overheat. No cloth is needed such as when you use an iron.
Petroleum jelly or mayo seems to be popular. Just apply the mayo or petroleum jelly onto the white marks using a clean cloth.
You may need to leave it on for an hour or even overnight.
Have several soft clean cloths ready to wipe off the mayo or petroleum jelly and keep wiping and buffing until the top feels smooth.
This site has several other suggestions so hopefully one will work for you as you may not have every product suggested available.