There is indeed a special immigration court system, but there's a catch. Those courts are "administrative courts", meaning that they are formally part of the executive, not the judiciary, and judges are also executive appointees. So they operate under rules that are themselves written by ICE, and with this admin's insistence on "unitary executive" theory, are entirely subject to the whims of the president.
To give you one example of how bad it already was before Trump, these are the same courts where 3-year old children who don't know English were required to argue their case before the judge by themselves, without a lawyer: https://www.snopes.com/fact-check/children-immigration-court...
So it was already a sham as far as due process go. But now the executive says that they aren't obligated to give people a hearing at all.
And anyone working for ICE is a willing enforcer for this system. They should be treated accordingly.