This is the advantage of only using an antiquated, pre-modern translation -- you don't have to acknowledge such things.
When it is missing altogether from one very well respected and thought to be mostly complete early version of the Bible it should more than pique one's interest. When it is totally missing from another even older version, but again very well respected, it is time to start thinking awfully hard about that particular passage. I have a feeling that it is missing from even more than those two.
EDIT: My feelings were justified:
"To be sure, the story is often marked out in various ways in both scholarly editions and Bible translations, for example, by double brackets and an accompanying footnote explaining that it is missing in the earliest manuscripts, including Papyrus 66, Papyrus 75, Codex Sinaiticus and Codex Vaticanus from the third and fourth centuries, and goes unmentioned by Greek church fathers until the twelfth century."
Does the Woman Caught in Adultery Belong in the Bible? | Tommy Wasserman
The source is a Christian group. Now it may have appeared in other "gospels" but not in any of the four:
"
Eusebius (c. 260–c. 340) in his church history attributes a similar story to Papias of Hierapolis (c. 60–130) and the now lost
Gospel of the Hebrews. Further, Didymus the Blind (c. 313–398) says he found the story “in certain gospels,” a reference which likely suggests he did not know the passage from John, but from a different gospel.
Codex Bezae (c. 400 AD) showing a later dash mark in the left margin at the start of
John 7:53 (
f. 133v)
The earliest manuscript evidence for the passage in John is the Greek-Latin Codex Bezae (c. 400 AD) which contains the story in its traditional place both in Greek and Latin on facing pages. Interestingly, later annotators have marked out the story in the margins, probably because it was treated separately in the liturgy."
It goes on to mention some other possible sources. None of them John.