'I need to return home.' should be accepted although return is not an option in the word tiles exercise.
I agree completely I need to return home is a much better English than I need to go back whole.
Casa can be used without an article to mean "home" rather than "the house".
- a casa, de casa, en casa - (to) home, from home, at home
- a la casa, de la casa, en la casa - to the house, from the house, in the house