..if this is the case,..the palm(s) may already be in decline...damage of any sort to any area of the trunk of 99% of palms..especially if repeated over time is generally fatal to them..
Remember that palms do not produce bark or a cambium layer..and do not heal or "compartmentalize" injuries like plants with woody tissue will..A palms trunk is just a mass of hardened spongy material which has expanded as the tree has grown taller..unlike a typical tree which will form annual growth rings as the tree matures..
If the damage is severe, and the tree is declining, you will notice it grow weaker with time..and that can take a couple years with some species.
As for patching any damage..dont..you will only increase the spread of any fungal pathogen which has already entered into the tree..allow the tree to decline on its own..then shoot your gardener