You can rub them with a tennis ball and they should come right off! Wipe clean!
A pencil eraser should work too!
Thank you for the tips
a Magic Eraser should do it. :)
The easiest way to remove black shoe marks is with the Mr Clean Magic eraser cleaning bars. Use gloves though, and DO NOT let a small child handle the cleaner, it can cause a burn type rash on small children. Like all cleaners, best to keep them out of reach of children. However, it WILL clean up the linoleum. A janitor I know uses them constantly in cleaning the school lunchroom and also other rooms.
Fantastic brand cleaner works also. I have the one with bleach in it, but shouldn't be necessary.