The passage in question was (most likely) not part of the Gospel According to John, instead of being added later. It is the most significant text theologically that might have been added.
The Codex Vaticanus, either the oldest or second oldest full New Testament manuscript we have, omits this passage.
The Codex has been around with Western Catholic and possibly Eastern Orthodox churches since it was written.
The Codex was not paid attention to much (Catholics are not Sola Scriptura believers so they care less about the bible) until a scholar "found" it in the Vatican library. That codex as well as all other ancient manuscripts omit it.
In my opinion, the oldest manuscript we have with 100% of the New Testament in Greek (yes, Revelation is there too, just not written by the same copyist at the same period) is what God would use to preserve the accurate form of scripture.
Other reasons to think the passage is not original exist too
- it cuts the flow of the narrative in John.
- it has been added in other parts of that area in John as well as into Luke with the same text.
- the story makes little sense (what is Jesus writing in the ground?
Also, until Jesus died on the cross, the Law that Jesus goes against WAS IN EFFECT IN ISRAEL, as seen in the rest of scripture where Jesus says that all the Torah should be kept and teaches the most extreme way to understand it in the sermon on the mount. Only after he died, is the law not applying (it was given because of transgressions until the seed comes according to Galatians).
One thing I do need to stress - the New World translation is one of the worst ones out there and is used and writen by followers of a heresy that denies that Jesus is YHWH, and uses YHWH name in vain. Literally, any translation is better than that one.