sin offering: The Hebrew word is the same as the sin offering (khatta’t, see study note on Leviticus 4:1–5:13). Some scholars think this offering was only for purification or decontamination, including cases mentioned in Leviticus 5:1–6.
This offering here was part of a purification ceremony. But it is more probable that the sin offering addressed a lack or failure. In this context, the focus is on purity rather than sin. It is meant to restore the woman to community fellowship, not to forgive a sinner.