The revelation comes to light in a new BBC documentary on the sudden departure of the nun and four of her Sisters of Charity 18 months after arriving in the troubled Ballymurphy estate in Belfast in October 1971.
The parish of Ballymurphy developed an extraordinary bond with the iconic nun.
Now, 40 years on, residents are convinced Mother Teresa left after being made to feel unwelcome by the late parish priest, Canon Padraig Murphy, who died in 1988.
In the documentary Mother Teresa 123 Springhill Avenue, the church insists Mother Teresa left her modest home on 123 Springhill Avenue of her own accord.
But Sister Eileen Sweeney, who arrived in the terraced house the day after Mother Teresa's departure in 1973, said a torn-up letter written by her reveals the true reason behind her exit.
Sr Eileen said: "Soon after I tried to put the pieces together. In the letter she started off by saying: 'Bishop I feel sorry for you. What you said was most unkind . . .'
"And then toward the end she said she wanted to make sure there wasn't a lot of bad feeling left in the community because of the nuns being told to get out. Where that letter is now God only knows."
Father Des Wilson, who was one of the people involved in inviting Mother Teresa to Ballymurphy, said parish priest Canon Murphy never quite approved.
A close colleague of the late Canon Murphy, Fr Sean Murphy, said they did not see eye to eye.
He said: "He had a saying that Ballymurphy was very different from Bangladesh. There is poverty in both places but they are different types of poverty."
The late Canon Murphy died without ever openly speaking about her departure.
A spokesperson for the church, Father Edward McGee, said they found letters in the archive written by Mother Teresa that say she left Ballymurphy of her own free will.
Local resident Gerard Kelly, who was 16 when the nuns arrived, said the church should apologise for its treatment of the nun.
'Mother Teresa 123 Springhill Avenue' will be shown on BBC One tomorrow at 10.35pm.