To overturn it, they either need to demonstrate some flaw in reasoning that would invalidate the prior court's ruling, or they need to openly declare the the POTUS is not an officer of the United States and thus is immune to any restrictions or laws that apply to the candidacy to such offices, like the 14th Amendment. That anyone who's led an open rebellion against the USA must be allowed to run for President, even if they couldn't run for any other position in government.
The former's not necessarily easy, and I find the latter so wildly unlikely as to not be a real consideration.