But don’t be too hard your friends. A 2009 Pew poll found that 22 percent of Christians in America believe in reincarnation. And many Catholics who believe in rebirth share your friends' belief that because the Church has never officially condemned it, this means she may one day reconcile reincarnation with the Christian concept of death and the afterlife.
However, this is a misunderstanding that Cardinal Christoph Schonborn addressed in his book, From Death to Life: A Christian Journey, where he writes:
“Why has Christianity always rejected the idea of reincarnation? As far as I know, the Church has never formally condemned the doctrine of reincarnation: not because she might regard it as a doctrine that could be compatible with the Christian faith, but on the contrary because reincarnation so obviously contradicts the very principles of this faith that a condemnation has never seemed necessary.”
As he points out, Church teaching on the subject of death and the afterlife could hardly be more clear. “Death is the end of man's earthly pilgrimage, of the time of grace and mercy which God offers him so as to work out his earthly life in keeping with the divine plan, and to decide his ultimate destiny. When ‘the single course of our earthly life’ is completed, we shall not return to other earthly lives: ‘It is appointed for men to die once.’ There is no ‘reincarnation’ after death.” [Catechism No. 1013]
This teaching comes straight from Scripture in the Letter to the Hebrews which responds to the question of whether or not there is more than one lifetime. It clearly states that it is “appointed for mortals to die once, and after that the judgment.” [Heb 9:27]
Thus, Catholics believe that “Each man receives his eternal retribution in his immortal soul at the very moment of his death, in a particular judgment that refers his life to Christ: either entrance into the blessedness of heaven—through a purification or immediately—or immediate and everlasting damnation.” [Catechism No. 1022]
For a Christian, there's no need to come back and work out our bad karma. Our bad karma was nailed to the cross of Jesus Christ, who took our sins upon Himself and reconciled us to the Father.
In other words, we don't need a re-do.