The correct option is C off
The context refers to the action the doer does with the object when she comes home.
"To take off" something, in this case the shoes, is to remove or discard that thing. So, in this context she removes her shoes (from her feet) when she enters the house. Thus, this is correct.
"To take on" something is to accept a challenge.
"To take in" is to give someone shelter.
"To take of" is grammatically incorrect in this context.
Thus, option C is the correct answer.