Meaning of the biblical quote at the end of Raging Bull?

The quote both relates how, by the end of the film, Jake LaMotta has found his own peace; and as a tribute to Martin Scorsese's film teacher, Haig P. Manoogian.

Filmsite's review of Raging Bull says:

The final title commemorates Jake's "once I was blind and now I can
see" salvation and new understanding:

Final Title:
So, for the second time, [the Pharisees]
summoned the man who had been blind and said:
"Speak the truth before God.
We know this fellow is a sinner."
"Whether or not he is a sinner, I do not know,"
the man replied.
"All I know is this:
once I was blind and now I can see."
John IX. 24-26
the New English Bible

Remembering Haig P. Manoogian, teacher.
May 23, 1916 - May 26, 1980.
With Love and resolution, Marty.

Remembering Haig P. Manoogian, teacher. May 23, 1916 - May 26, 1980. With Love and resolution, Marty.

[Director Martin Scorsese's dedication to his NYU film teacher.]

Film Reference says:

Martin Scorsese's telling of the story of Jake La Motta has given rise to a number of different, often conflicting, readings. For Scorsese himself, La Motta's trajectory from promising boxer to middleweight champion of the world to night-club performer is the story of "a guy attaining something and losing everything, and then redeeming himself." Such a reading is clearly reinforced by the quotation from St. John's gospel preceding the final credits, which tells of a man whose sight has been restored by Christ rebuking the Pharisees: "Whether or not he is a sinner, I do not know," the man replied. "All I know is this: once I was blind and now I can see." On this level, La Motta's life becomes a kind of spiritual odyssey of the kind encountered before in the work of Schrader and Scorsese, both separately and in collaboration one with another. As Scorsese describes La Motta: "He works on an almost primitive level, almost an animal level. And therefore he must think in a different way, he must be aware of certain things spiritually that we aren't, because our minds are too cluttered with intellectual ideas, and too much emotionalism. And because he's on that animalistic level, he may be closer to pure spirit."

However, it wasn't how the script originally ended. From Les Keyser's Martin Scorsese (Twayne Publishers: New York, 1992), pages 121-122:

The title cards with which Scorsese chooses to end Raging Bull suggest that he did not feel equivocal about La Motta's salvation. The original script ended with images of Jake shadowboxing, a description of Jake as "still alive, still a condender, a forty-two year old man fighting for a shot," and a citation from St. John's Gospel, chapter 3, beginning with verse 3: "Verily, verily I saw unto thee except a man be born again, he cannot enter into the kingdom of heaven." By the time Raging Bull was completed, Scorsese decided to change the citation to later lines in St. John's Gospel, chapter 9, beginning with verse 24: "So, for the second time, the Pharisees summoned the man who had been blind and said: 'Speak the truth before God, We know this fellow is a sinner.' Whether or not he is a sinner, I do not know,' the man replied. 'All I know is this: once I was blind and now I can see'."

Scorsese was totally responsible for the new text. His collaborator [screenwriter] Paul Schrader maintains that it does not fit the film: "I had no idea it was going to be there, and when I saw it I was absolutely baffled. I don't think it's true of La Motta either in real life or in the movie; I think he's the same dumb lug at the end as at the beginning, and I think Marty is just imposing salvation on his subject by fiat. I've never really got from him a terribly credible reason for why he did it; he just seemed to feel that it was right" (Schrader 1990, 133).

In this new "now I can see" citation, Scorsese was commemorating Jakes' new understanding and peace, but as his title card went on to note, he was also "Remembering Haig P. Manoogian, teacher, May 23, 1916-May 26, 1980, with love and resolution, Marty." Those who knew Manoogian would recall that he challenged all his New York University students to see and linked the idea of seeing with the essence of art and religion. As a headnote, for example, to his text The Filmmaker's Art, Scorsese's mentor had cited the Victorian critic John Ruskin: "The greatest thing a human soul ever does in this world is to see something, and tell what it saw in a plan way. Hundreds of people can talk for one who can think but thousands can think for one who can see. To see clearly is poetry, prophecy, and religion, all in one" (Manoogian, vii). Scorsese found poetry, prophecy, and religion in La Motta's life and struggled in Raging Bull to make audiences share his vision.