It's not something that everyone has to deal with, but for those with children that put everything in their mouths or for those with animals that like to gnaw on things, teeth marks on furniture are an issue. These marks can get unsightly after a while, but there is no need to replace the furniture. It is possible to salvage the wood with a few simple supplies.
Place a slightly damp cloth over the bite area. This will work if the bite marks are not deep into the wood.
Set an iron on a medium setting and place it on the cloth.
Iron the cloth to heat the damp rag and create steam. Continue ironing for a couple of minutes.
Remove the rag and look at the dented area. If the bite marks are raised, then you are done. If not, repeat the process.
Polish the wood as normal to bring back the shine.
Lightly sand the surface of the bite mark area with a fine sandpaper such as 220 grit.
Wipe the area with a damp rag to remove dust and let it dry.
Fill the holes in with wood putty and let it dry. Sand the surface to even it out with the rest of the wood once it is dry.
Wipe on a wood stain that matches the rest of the furniture surface. Let coats dry and apply as many as needed until it is the same as the rest of the piece. Let the stain dry.
Brush on a clear finish if the rest of the furniture has one. If not rub with furniture wax to create a shine.