How do you remove a burn mark in light wood?
Method 1: Using the finest steel wool available, rub the smallest area possible --- in the direction of the grain -- with mineral oil.
Method 2: Soak a cork in turpentine and then rub the burned area with it. Once the burn is eliminated, apply a coat of wax over the spot.
If you have waxed wood, then use a piece of cork soaked in turpentine and rub the burned area with it; once the wood burn is gone, put a coat of wax back on the wood.
Lacquered wood: on modern lacquers, clean with a cloth dampened with soapy water, and if the burn stains resist add a few drops of household alcohol or bleach; on a more fragile lacquer pass a cloth impregnated with a mixture of 1/3 of gasoline and 2/3 of linseed oil.
Varnished or Vitrified wood: remove the burn marks by scraping the wood with a knife blade and then fill the hole with a wood paste in the color of the furniture; rub gently with sandpaper to even the surface then apply a varnish of the same color; or run a cloth impregnated with a mixture of 1/3 gasoline and 2/3 linseed oil on the stained varnished wood.
You would have to sand down the area, apply the stain and then the topcoat. If this is a large or visible area you will have to do the whole thing, such as a dining room table top.
First I would try light sanding right atop the burn then I would use a furniture marker as close to the same color as possible.
First clean your table.
Then mix a generic baking soda and a non-gel variety of toothpaste in a small bowl until it is a sticky paste.
Put the paste over the heat mark and give it a few minutes to set.
Burn marks also come off easily with a mixture that's equal parts linseed oil and Rottenstone Polishing Compound. Mix them in a bowl until a paste is formed, and with a clean rag, rub this paste onto the afflicted area of your wood. Make sure that you rub along with the grain of the wood as you go. After the paste has been applied, leave it alone for up to five minutes. After it has had time to set, wipe it away with a clean and damp cloth. You may need to continue to do this until the burn mark is gone.