I checked page 370 of the out-of-print book titled, Adoption Agencies, Orphanages and Maternity Homes--An Historical Directory, and it lists Convent of the Good Shepherd in Memphis, founded in 1875.
In 1922 it housed 207 delinquent teenage girls. I have a feeling it did not admit girls who were not Catholic, but I'm not sure.
Institutions of similar name occur in many cities, operated by three Catholic orders of nuns. The name Good Shepherd was used for a few Protestant institutions, but not in Tennessee, as far as I know.
I believe the girls were committed to the House by a court order, but I do not recall anyone saying they had done such research in a court index.