This is just a verbose explanation of slim's post above, so skip it unless you want mind-numbing detail.
In the Introduction to the 1984 NWT Reference Bible it says that the basic Greek text used was The New Testament in the Original Greek, by Westcott and Hort (W&H). The Greek texts of Nestle, Bover, Merk and others were also considered.
Quite simply, W&H did not include episkopountes in 1 Peter 5:2 and the translators of the NWT concurred. Why did they not include it when there was sufficient reason for the King James Bible to translate it as "taking the oversight thereof" in 1611? Because they concluded the early mss did not support it.
In the Appendix to the W&H Greek text there is a section Notes on Select Readings which include "miscellaneous rejected readings sufficiently interesting to deserve special notice". The rejected reading of episkopountes at 1 Peter 5:2 is included and the notes are shown here:
What does that mean? That there is quite a lot of support for episkopountes, but manuscripts without it include Sinaiticus (original reading) and Vaticanus 1209, and W&H maintained that when these two important witnesses agreed on a reading then it was usually given more weight than alternative readings.
Although the Emphatic Diaglott is based on Vatican 1209, the codex doesn't have episkopountes at 1 Peter 5:2 and so the Emphatic Diaglott has the word in square brackets to show it's not in the main text.
How was the basic Greek text of 2013 Revised NWT different to the 1984 translation? The Watchtower of 15 December 2015 explained (p.17):
The original New World Translation was based on the Hebrew
Masoretic text and the respected Greek text by Westcott and Hort. The
study of ancient Bible manuscripts has continued to advance, shedding
light on the reading of certain Bible verses. Readings from the Dead Sea
Scrolls have become available. More Greek manuscripts have been
studied. Much updated manuscript evidence is available in computer
format, making it easier to analyze the differences between manuscripts
to determine which reading of the Hebrew or Greek text is best
supported.
Probably consideration of Papyrus 72, which is the earliest known manuscript of this letter (and can be viewed at the Vatican Library here [p.20, top of the page]), revised their judgment on this.