alt Hacker NewsSCOTUS can't just "invalidate" an Executive Order like how they can invalidate an unconstitutional law (judicial review). The court system doesn't work like that. No one would have standing to bring such a case, nor does the judicial branch have authority over executive branch internal communications.
What could happen is that a federal agency follows an EO in a manner contrary to law, and that action causes some sort of harm or loss to a person. That injured party could then bring a legal action against the agency and the Court could order the agency to cease that action. But it still wouldn't invalidate the EO.
EOs are subject to judicial review. Whether it's a law or an EO someone typically needs standing to challenge it. Although, you can even have Congress create a resolution allowing that. Frankly, there's nothing wrong with the wording of the current EO. What is more likely to be challenged are any rules that come from that EO that run counter to the law.
"But it still wouldn't invalidate the EO." Truman and the steel mills would disgree.