I was Very intrigued by this question and found This http://bl-libg-doghill.ads.iu.edu/gpd-web/historical/Reportontheofficeofcensorship.pdf Report. It was commissioned by FDR and given to him by the Director of Censorship. Who give an amazing introduction That includes this paragraph

The first and last principle to be remembered, then, is that censorship should come into being solely as an instrument of war It must charge itself only with contributing to the success of armed combat. To the extent its operations are permitted to wander into other pathways, to the extent it concerns itself with the enforcement of peacetime statutes or the policing of political and personal foibles,-to that exact extent does it weaken its service to the nation's armed men on the field of battle.

It also seems that this director Byron Price ,A former AP Washington Bureau Chief, Got a Special Pulitzer for creating the codes of censorship used during the war.

Follow up question: were any similar challenges made against the Hayes code?

Keep in mind that WWII was the last time that that the United States actually declared war and had been declared war upon. Most interpretations of the Constitution hold that in such situations, the President has broad executive power to protect national security. That includes emergency actions like creating an ad-hoc agency to protect sensitive information relating to wartime activity. The constitutionality of the Office of Censorship was never formally challenged during its four year life.

But tasking a government agency with the ability to censor information is quite an affront to First Amendment principles. To get around this, FDR appointed AP's Washington bureau chief Byron Price to head up the agency, which Price agreed to on the condition that all censorship in the media would be voluntary. FDR wasn't as concerned with subversion and dissidence in the press as much as he was with sensitive information being inadvertently reported on or transmitted, particularly if an enemy agent was trying to disseminate a coded message in the news media. To that end, Price established guidelines for journalists that were voluntarily complied with almost universally: "man on the street" radio interviews, call-in programs, classified ads, etc. pretty much ended during WWII. Reporting on the weather and presidential travel was limited too.

There were a few instances when these guidelines were violated, usually by accident, and the government did not attempt to press charges on the parties involved. It's perfectly constitutional for the government to ask reporters to not report certain things, which is what the government essentially did and continues to do to this day.

What's really interesting is that the Office of Censorship was immediately closed after Japan's surrender. It fulfilled an emergency purpose and no one wanted to see it continue.

The Office of Censorship and the press's compliance with the government is still hotly debated in media ethics. The perceived role of the press has changed quite a bit since WWII. Prior to the Vietnam War, the news media in the United States was incredibly deferential toward the government, especially when it came to matters of national security. Today, we expect the press to act as a mechanism to hold the government accountable, but during WWII, there was an expectation that the press should do its part with the war effort.

Source: Sweeny, Michael. Secrets of Victory: The Office of Censorship and the American Press and Radio in World War II. 2001.