There are some questions about the authenticity of
Pericope Adulterae.
Jesus and the woman taken in adultery - Wikipedia
Those questions aside, I agree the verses fit with the overall message and intent of Christ that marked a radical departure from Mosaic law. This was now an the emphasis on a much more personal relationship with God. The implications were that we should now keep our innermost thoughts pure from defilement, bnot just obey the law outwardly. In that regard, Jesus talked about the very thought of lusting after a woman as adultery in one's heart (Matthew 5:27-28).
The
pericope adulterae is of very ancient provenance and was canonized by the church as scriptural, whether or not it properly belongs in the Gospel of John. I'm just glad the scribes found a place for it somewhere if it isn't original to the text!
Eusebius describes how Papias, an early apostolic father born in the first century who had contact with the apostles, composed an authoritative compilation of the authentic oral tradition of Jesus that hadn't made it into the four gospels.
The story of a woman accused of serious sin before Jesus, which practically all scholars take to be the adulterous woman, features in Papias's now lost book on the
Sayings of the Lord and was also apparently featured in the Jewish
Gospel of the Hebrews, again very early and containing canonical traditions like the resurrection appearance of Christ to his brother James.
The latest scholarly treatment of the PA, which has since become a university textbook, is an edited book,
The Pericope of the Adulteress in Contemporary Research. (T&T Clark, 2016.), that pulls together five academic contributions from experts, two who are in favour of the PA's authenticity and three who regard it as a scribal interpolation.
Even those scholars who argue for it's inauthenticity as an original part of John, freely concede that it's ancient. Wasserman, for example, notes that a story of an adulterous woman was known among Christians in the second century, and already established by then.
St. Augustine of Hippo came up with the so-called "
suppression theory", according to which certain scribal copiests tried to delete the PA because they worried it excused adultery and was too sympathetic to women. He wrote:
Some of little faith, or rather enemies of the true faith, I suppose, from a fear lest their wives should gain impunity in sin, removed from their manuscripts the Lord’s act of indulgence toward the adulteress, as if he who had said “sin no more” had granted permission to sin. (Augustine, De Adulterinis Conjugiisii.6-7)
In that scholarly compilation I mentioned above, Professors David Punch and Maurice Robinson argue in Augustine's favor.
So, there is no overwhelming consensus on whether or not the
adulteress woman narrative was an interpolation (although you might say the majority opinion tilts that direction).
I don't fall down clearly on either side of this dispute, because as a Catholic it doesn't really matter to me. Sacred Tradition is an authoritative source of Divine Revelation in my church and the PA has been universally endorsed by the Magisterium as apostolic in origin.