Clinton was on a 3-day visit to India from May 7.
This was the first-ever visit by a US Secretary of State to Writers' Buildings to hold a meeting with a chief minister.
Both Clinton and Banerjee are listed among the 100 top influential people in world by Time magazine.
In her keynote address after receiving Century Award at the New York Women's Foundation Breakfast, Clinton termed her trip to Kolkata as remarkable.
"I went last week to West Bengal in East India and had two remarkable experiences