Thanks, gang. It was real, "Old Fashioned" milk paint, not faux milk paint. As I recall, it has a couple of coats of polymerized tung oil over it. I like the suggestion to run a full test on a scrap piece first - dry milk paint, sharpie, then see what works, or what's necessary, before touching the bowl. Will report back.
In my favor, it's a single, standard color. Not in my favor, I have cut flutes into the paint, so repainting the whole thing isn't really an option.
Does anybody have any experience with Amodex stain remover?
The photo was taken before the mark was made.