smear [transitive] to spread an oily or soft substance over a surface in a rough or careless way SYNONYM daub
smear something on/over something The children had smeared mud on the walls.
smear something with something The children had smeared the walls with mud.
His face was smeared with blood.
scrub something off | scrub something off something
to remove something from the surface of an object by rubbing it hard with a brush, etc.
This treatment involves scrubbing off the top layer of dead skin.
wipe: to remove dirt, liquid, etc. from something by using a cloth, your hand, etc.
wipe something (from/off something) He wiped the sweat from his forehead.
wipe something away/off/up She wiped off her make-up.
Use that cloth to wipe up the mess.
A kid tried to write or smear the ink of a marker all over his hand.
Do you say to him "Don't smear the ink of the marker all over your hand. It sticks hard on your hand. Now I have to scrub / wipe it off your hand"?
I am not sure using "smear" and "scrub / wipe" is idiomatic in this case. "Wipe" seems too weak to remove the ink.