Explain to us exactly what it is you think the court system can do and where it gets the authority.
The U.S Constitution enumerates only 1 method of removing a sitting President. That is impeachment. The court cannot compel Congress to impeach the president.
I had a fantasy though, fantasy argument. The Chief Justice of the SCOTUS can remove the President because he administered the oath of Presidency and Obama has verifiably broken that oath by failure to execute the laws of the United States.
An ineligible person is not president.
The court can define the qualifications laid out in the constitution. Then I agree congress would have to act to remove him.
I would add that the various Secretaries of State did not do anything on this issue.
We are slowly and surely losing the idea of being a nation of laws and just one of political power. Maybe we have always been that way
If Obama was never eligible, he never lawfully occupied the office. So, the procedure would to remove him would be the same as removing an someone pretending to be the POTUS. Federal Marshals drag him out by the ear.
There is plenty of legal precedent for this position.
The open question would be if Biden is legally the VP, and therefore the successor POTUS.
Impeachment does not remove. Conviction removes.
The House impeaches, the Senate convicts.
Impeachment is akin to indictment.
Senate convicts is actually more akin to Senate removes by presenting facts for a vote in which Senators act as judge, jury and executioner; executioner in the sense of removing from office but not for imprisonment.
Once removed by the Senate, the judicial branch may try to convict in a court and this can result in imprisonment.