This question is really about the history of a phrase, not about who is famous for using it in Indian courtrooms.
Once the question is read carefully as asking about the term's first use rather than about who expanded PIL in India, the two Indian judges and Professor Baxi fall away, leaving only the scholar credited with the phrase.
So, the correct answer is Prof. Abram Chayes.
Legal history sometimes separates the person who names an idea from the people who later put that idea into wide practice, and this question is testing exactly that distinction for Public Interest Litigation.
Keeping the distinction between naming a concept and expanding its use in mind, the phrase itself is traced to Professor Chayes, while the Indian names belong to the story of how PIL was practised and grown.
Hence, the correct answer is Prof. Abram Chayes.