Where does anyone get the idea that someone ineligible to the office of President can ever be President?
You can remove a President in one of four ways:
But if he's not eligible, he's not President, and never was. Elections, oath taking, etc aside. No one, No One, has certified his eligibility, only his election. The votes were properly cast, but properly cast electoral votes cannot make someone who is not eligible, suddenly eligible. Impeachment is for President, not ineligible usurpers.
The courts get their powers from Art. III of the Constitution, which says in part:
You can remove a President in one of four ways:
...
Section. 2. The judicial Power shall extend to all Cases, in Law and Equity, arising under this Constitution, the Laws of the United States, and Treaties made, or which shall be made, under their Authority;
This would be a case arising under Article II of the Constitution, and thus the federal courts have jurisdiction to decide it.
Just a hunch, maybe because the Chief Justice of the United States, the rest of the Supreme Court, the leaders of both parties in the Congress, the former President, and the Commissioned Officer Corps of the United States believe that he is President. You might want to contact all of them and let them in on your big secret.
Placemark.