Which Sufi teacher was also known as the ‘Gharib Nawaz’?

The correct option is Khwaja Muinuddin.

Khwaja Muinuddin Chishti was a highly revered 12th-century Sufi preacher, scholar, and philosopher from Sistan (modern-day eastern Iran/southern Afghanistan) who eventually settled in Ajmer, Rajasthan, India. He is widely credited with establishing the Chishti Order (Chishtiyya silsila) of Sufism in the Indian subcontinent.

He came to be popularly known as 'Gharib Nawaz', a Persian title which translates to "Benefactor of the Poor" or "Cherisher of the Poor". This title was bestowed upon him due to his deep compassion, humility, and lifelong dedication to serving the destitute, poor, and marginalized sections of society, irrespective of their caste or religion.

Let us briefly look at the other options to understand why they are not correct:
1. Shaikh Nizamuddin Auliya: A prominent disciple of Hazrat Baba Farid, he is famous by the title 'Mahbub-e-Ilahi' (the beloved of God).
2. Amir Khusrau: An iconic disciple of Nizamuddin Auliya, he was a legendary Sufi musician, poet, and scholar, often referred to as the 'Tuti-e-Hind' (Parrot of India).
3. Shaikh Qutbuddin Bakhtiyar Kaki: A major disciple of Khwaja Muinuddin Chishti, after whom the Qutb Minar in Delhi is believed to be named.

Therefore, the title ‘Gharib Nawaz’ is uniquely associated with Khwaja Muinuddin.