My dining table has some grayish spots caused by a steam iron. How do I fix?

1. species of wood, and solid or veneer?
2. finish (e.g. polyurethane on a non-antique) and is it stained or clear?

If you don't know and don't want to pay someone experienced in all this, and don't want to power sand down the whole top and refinish, then lightly sand just the spots using your finger and a small piece of 100 grit paper and then 180 grit, and rub on a matching pigmented polyurethane (smallest can sold) with a tiny piece of cloth and your finger. It won't be perfect. But grey means that the water damage didn't go through the finish and into the wood, so that's good.

No, it won't be perfect. It will look perfectly awful. Trust me, tried that, not exactly as stated. I know wood refinishng and the only way is having the table professionally refinished. Sorry. Wood restoration is my hobby !

Try buffing it with cigar or cigarette ash and a terry towel.