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Trump doesn't need to recognize the Court's authority in this area even the supreme Court but I can see why he might want to get a ruling from the supreme Court to support his position as described here

"In its request, Solicitor General D. John Sauer said that the district court did not have jurisdiction to enter its order because federal immigration law leaves parole-termination decisions to the discretion of the Homeland Security secretary. Sauer said the district court lacked the authority to "usurp the Executive Branch's control of foreign policy and immigration."

but if the supreme Court does not rule in Trump's favor it makes it a little harder for him to ignore the courts but he still should ignore the court because seating executive branch authority to the courts would be unconstitutional and a huge mistake.

This is of course assuming Trump ever intended to do what he said and isn't just using the courts as his excuse why he doesn't do it.