A dent will steam out. Wood that has been removed such as the case you are showing will not steam out. You can raise the wood but when it dries the hole will be there again. Fill the spot with thick super glue, when it dries good sand it flush. After the finish is applied it will be very hard to see. If you intend to stain the gun, Stain that area before you fill it with the super glue.
Dents steam out. Holes do not steam out.