If it really bugs you, buy another gun. Even if you could get it removed at a reasonable cost, you will always know it had been there and will always be able to "see" it.
Back in the 70's I guess it was, "everybody" was telling us to engrave our SS number on everything. Police depts, insurance companies, etc, would loan you an electric pencil, or you could buy them for ten bucks at every place you could think of including 7-11. Protecting your personal information wasn't a big deal in those pre internet days. Heck, people put their names on mailboxes back then too. I too, was young and dumb and engraved mine on more than one gun, but I at least had enough sense to put in in some hidden place, like under the grips. Never occurred to us (me anyway) that there was already a unique serial number on the gun, TV, most everything really. Well....Duhhhhhhhhhh. Who knew?
Every time I see a used Model 19, I'll ask to pull the grips. Who knows? Maybe it will turn up some day.