I do restorations on milsurp rifles that sometimes look like that they were used as a cricket bat. Wet cloth and the cloths iron works well on light dings, but for many that I tackle I need to use a tea kettle on the stove and put the dent right over the spout. The steam swells the fibres and pushes them back out. Several treatments over several days is sometimes needed. Steam removes the finish and makes clean patches.
Even more drastic is my steam chamber, a wooden box with a hose fed from a pressure tank on a coleman stove. Heat helps sweat cosmoline preservative out of the wood and raises 99% of the dings.
In extreme cases where the woodwork is all but lost, I use a hot cycle in the dishwasher. Not recomended on delicate or thin sections of stock as warpage could result. Milspec stuff seems to return to normal shape after drying for a few days. Warpage or poor fit have never been a problem.
As mentioned, if the fibres are cut or gouged, steaming might improve but won't remove.