Were SCOTUS to say that, i.e., De Vattel’s Law of Nation’s held sway over the Framers and that is what they understood to be a “natural born citizen,” i.e., someone born within the jurisdiction of two citizen parents (unless serving the nation abroad), anyone not meeting that requirement wouldn’t make it to the electoral college stage, so the House wouldn’t be brought into play. As it is anyone with even a claim to citizenship by today’s understanding can run, be elected and serve as POTUS.
Where in the Constituton does it give the Supreme Court jurisdiction to tell the electoral college that they can't elect some individual as president?
They have no jurisdiction at all in regard to the eligibility of any single person that the electoral college elects. Congress is charged with determining whether or not the electoral college results are certified. If Congress determines that the person who was duly elected is not "eligible" then they can say so at that time. Once they certify the election, the only way to remove the President is by impeachment.
I guess the Constitution is only important if it keeps a solid conservative like Cruz out of office, eh?