In fact, Manfred's fruitless encounter with a priest comes much earlier in Byron's poem, perhaps indicated by Tchaikovsky by the chimes heard late in the 3rd pastoral movement, which primarily reflects Manfred's discussion with a peasant farmer.
At the end of the poem, Manfred cheats both the underworld demons and the church of his soul, despite the appeals of the priest who has rushed to the scene asking him to accept God in his final moments. Using his last magic trick, he ends his life; as the priest says in the final sentence of the poem: "his soul has taken its earthless flight; Whither? I dread to think, but he is gone".
Tchaikovsky apparently felt that this was too dark a finish for his title character, and therefore inserted the church-like chorale with organ, followed by the peaceful conclusion as an indication that despite his crimes, Manfred had somehow achieved positive redemption.
Mike Bosworth
Phnom Penh