Shapiro told Howell that in the decades since then, there has been an "evolved understanding" of how to interpret laws and that the outcome would be different today.
And the judge grappled with whether courts must defer to the House about when an official impeachment inquiry has begun.
Howell several times mentioned a brief filed in the case by Rep. Doug Collins of Georgia, the top Republican on the Judiciary Committee, that argued an impeachment inquiry only starts with a floor vote on a resolution to do so.
Letter responded that the House is in a formal impeachment inquiry "because the House says it is. The speaker of the House has said it is." And lawmakers are spending "one heck of a lot of time" on impeachment, Letter added.
There is also a resolution that authorized the Judiciary Committee to seek the grand jury material under its Article I powers -- which includes impeachment, Letter said.
Howell at one point said a House floor vote authorizing an impeachment inquiry would make it "easier for all of us."
And at another time the judge asked why the Justice Department did not think they could give the materials to Congress under a different exception to grand jury secrecy related to foreign intelligence and a threat of "grave hostile acts of a foreign power."
"I am curious about why I'm here, and why you're here in front of me," Howell told Shapiro.
Howell on Tuesday also demanded answers from the Justice Department about whether grand jury information from the Mueller report had been disclosed to foreign governments, and whether the department was providing information to the House as part of an agreement to give lawmakers access.
Shapiro said reports about FBI interviews from the Mueller probe were going to lawmakers, with redactions for "confidential communications" between senior White House advisers and Trump.