This is a question that has no answer. No one is going to put the name of the most secret unit in the MILITARY because THEY DON’T KNOW or they are not going to publish classified information on this site. But, there was a thread on Quora which had some straight answers and points to some units which are less known to the public but still doing the job. The people bring out a lot of unit names, but there were some misunderstands and wrong classifications of the units.
One of the authors, who described himself as a retired 27 year US Army Special Forces officer and enlisted soldier who have operationally served at the Team, Company, Battalion, and Group level, served in a training company at Special Warfare Center, been in two geographical joint commands, and combined joint Special Operations command overseas, has offered some answers.
First of all, he wanted to be clear and put the end to the discussions involving the CIA because they are not affiliated with the U.S. Department of Defense and thus; NOT A MILITARY UNIT. Any current discussion of CIA units and missions is speculation, at best. Further, he describes the definition of “Most Secret” which directly contradicts the question because it asked for the “Military’s most secret team”. He states “most secret teams are most probably”. Wait, that is not a referenced based factual answer. That is conjecture. As someone else stated, BS. Also, can anyone define “Underhanded” because I am not familiar with a military term such as that?
In his overview of the most famous units mentioned in the SOF community, he pointed out that both Delta Force (CAG) and U.S. Navy SEAL Team Six (ST6) are not considered Intelligence teams. Delta has never been referred to as a team while ST6 has been labeled a team from its original name.
People need to know the difference between the terms “Direct Action” and “Assault” used in SOF missions. “Direct Action” missions do not include Hostage Rescue. It is its own mission. “Direct Action” mission is not interchangeable with “Assault” mission. And of course, there is no such mission in US SOF as an Assault mission.
The most answers on the particular question lead to the ISA, despite it’s clear that they are not a military unit. But, the ISA at some point known as GREY FOX (one of the many identifiers they operated under in the last 20 years). As I have mentioned above, that is not the right answer because they are not under SOCOM but JSOC and they are not a Tier 1 SMU.