You ask a good question. There are only a handful of modern (non-KJV) translations that a householder would likely have. Among these are the TNIV (Today's NIV, revised in 2005) and the NRSV (1989). Both note that these verses, John 7:53 to 8:11, are not the product of the original gospel writer. The former sets the text off a bit with an introductory note and in different font and smaller type:
The latter uses double brackets and a note:
The revised NWT is not the first to simply "jump verses," or just not print the story at all. The Twentieth Century NT, J. B. Rotherham, Charles B. Williams, and Goodspeed's translation do as well. Here's the last mentioned:
Most other translations just leave verses out when a smaller block of text is involved, as for example, at Matt 23:14, Luke 17:36, Acts 8:37.
In all these cases the issue is the same. The chapters and verse numbers were added late in the Bible's history, in the late medieval period. By that time the Greek text had reached its highest point of corruption with the most additions and alterations. The KJV was based on such a Greek text. As time has passed since 1611, knowledge of what was likely the original text has improved and that has led to recognizing several passages as not original. The small examples immediately above as well as the large examples in John 8 and the end of Mark are all cases in point.
Therefore, it's better not to say that these verse are "removed" or "missing" but that they never belonged in the first place.