I remember back in the 1950's when the soles of my shoes made black marks on my mother's vinyl (linoleum) floor, she used Johnson's Paste Wax to remove the marks. It was in a round metal container about 4" in diameter and maybe 2" tall. Deep yellow in color. I think you can still buy the stuff.

Jay -
Ask on a doll collector's forum. You don't want to remove the arms along with the black marks.

LGarden, you are sooooooo right!!!!! I'm most afraid of removing the color of her arms along with the black marks!!
Miss Red, I have some of that very stuff!!!! I use it on my houseful of homemade furniture!!
Thanks to both of you!
Jaybird