Apparently there are multiple types of teargas. See link. Technically it is my understanding they shot pepper spray balls. Per the CDC, these are commonly referred to as teargas but is a different chemical compound than what the military typically uses abroad (but same effect).
The US Park Police did the clearing (not a branch of the military), but they appeared to be directed (or at least sanctioned) by Joint Chiefs of Staff, Gen. Mark A. Milley (the highest ranking military officer in the country), who walked with Trump, dressed combat fatigues. This was a purely domestic issue. Why was Milley there (and in uniform)? Trump has said he will use the military to put down violent protests if the governors can't handle it. Was he also merely a prop (like the Bible) or was he directing the response? Either way, his involvement is extremely distressing from a civil libertarian standpoint.
Link: https://www.factcheck.org/2020/06/the-semantics-of-tear-gas-versus-pepper-spray/