Here you go:
IT: This one depends on the context. At BC, IT is Intensive Training or Instructional Training; extra PT given to a recruit or a division as a corrective action (punishment). IT occurs when a Recruit, Recruits, or a Division need/s an extra reminder of what the Navy way to do things is. A session of IT cannot be longer than 45 minutes. IT is also Information Technology; the Naval community made up of communications experts who process, transmit and analyze a wide variety of data. IT is also the Information System Technician rating (https://www.cool.navy.mil/usn/enlisted/rating_info_cards/it.pdf).
ITE: Instructional Training Exercise. See also IT and Orange Card.
Orange Card: used by the RDC to issue IT when a recruit or division has exhibited substandard performance. (I can't find the current Orange Card, but here is a pic of a previous ITE card, which is the same thing and is still how ITE is given by the RDC in accordance with the procedures set down in the Red Book.) What does ??? mean? (A Guide to Navy Abbreviations and Terminology)
When my son went through basic training his division had a couple of time that they had IT-intensive training. I do believe one of the times, it was because they had a few in their division that believed that they did not have to be on time or up on time for anything. So the RDC used IT training to motivated not only those individuals but the whole division. It is meant to have them see that they are a team. Let me tell you after that time of IT those who were late had other division members making sure they were not.
By the way, they did the same thing when I went through bootcamp back in the late 90's. They just did not call it intensive training. They are not trying to harm anyone it is to make the division realize that they are team and work together as a team. One fails, they all fail because in the fleet out in the middle of the ocean. Shipmates have to be able to rely on shipmates.
I spoke with SR on the phone a few days after posting the question. Turns out, SR inadvertently added the "E" while 'hurry-writing' an earlier letter LOL. SR mentioned that although it's exercise (punishment or otherwise), in that division, it's mostly referred to as Intensive Training or "IT". :)