Beside the expiatory system there runs an entirely different account of how papa is cleared, and Hinduism has never required a reader to choose between the two.
The Bhagavad Gita closes its argument by setting the tariff aside. Krishna tells Arjuna to abandon all duties and take refuge in him alone, and undertakes to free him from all papas, telling him not to grieve. Read against eleven chapters of Manu, that is not a graded remedy at all. It is a transfer of the whole problem to somebody else, and the bhakti literature that follows takes it up: the Bhagavata Purana tells of Ajamila, a man whose life had been thoroughly disreputable, who at the point of death called out the name of his son, which happened to be a name of Vishnu, and was released on the strength of the utterance.
The two registers coexist. Pilgrimage, gift and vow accumulate punya in one; devotion and surrender clear papa in the other; and the argument over how much of the work belongs to the devotee and how much to God is live in the theistic schools, which the atlas tracks in its entry on grace and self-effort in Vaishnavism.
What the pair together do not amount to is sin in the Abrahamic sense. There is no single lawgiver whose command has been broken, even in the devotional register, where the language is of refuge and dependence rather than of acquittal. And the mechanism itself, though shared with Buddhism and Jainism, is understood differently by each: Jain teaching treats karmic residue as a material substance adhering to the soul, and Buddhism denies there is an enduring self for the residue to adhere to at all.