In this instance, “back home” does not mean “to go back home”. It simply refers to the girl in his home town/city/country i.e. where “he” grew up, where his parents are, etc.

Back home in this context means "back in my home town" and not "to go back home".

The girl waiting for him to return to her.

the girl was at home, "back home" refers to the girl, kinda "He kept his promise to the back home girl", that is "the girl who stayed at home"

back home回家