Which of the following statements is grammatically correct?

Option C is correct because "each" is a singular pronoun, so it requires singular verbs and pronouns. In this case, "had been ill-treated" correctly uses the past perfect tense to indicate that the ill-treatment happened before the abandonment. Also, since the focus is on each girl individually, the singular pronoun "her" is used correctly. 

Options A and B are incorrect because they use plural pronouns ("they" and "were"), which don't match with the singular subject "each." Option D uses the past perfect tense unnecessarily before the abandonment, making it grammatically incorrect.