How do I permanently remove a previous Mii from a 3DS when it is not in the Mii Plaza?

I brought a second-hand 3DS and when in the Mii Plaza, I am the only character, the favorite. But when I play Mario Kart 7, all the accolades show as the previous owner’s Mii even though her Mii is not to be found. How do I get the previous owner’s Mii out of the system, and set all games to use my Mii?