Hmmmm......this could be her in 1900 but really no way to be certain and there are no other McKenna's with her.
Mary McKenna Chicago Ward 34, Cook County, Illinois. born Scotland, parents born Ireland, Boarder, age 26, born May 1876, employed as a saleswoman.
Sorry but no immigration info on the 1900......and it's left off her 1910 particulars! By 1920 Frank is a widower but the girls are then stating their mother was born Ireland.
Not much help...
Jean