Well, I think it proper that Congress exercises oversight over the process. Just as we never get a declaration of war any more, I doubt we'll get a vote on the matter - but Congress still needs to participate in the process so they can establish the authority to rescind tribunals if a future president abuses them. We gotta look past the current crisis and contemplate the types of people (i.e., HRC) who would love to have these powers and no Congressional authority to stop them because Congress abrogated their powers...
They can simply enact their own legislation for the conduct of the tribunals.
This is their duty- to legislate where needed- and they have failed IMHO.