It would then be up to the kids to go to the American consulate, upon reaching their majority, to formally renounce their US citizenship (and nationality...they're not quite the same thing).
From what has been posted on FR supposedly from State Dept documents, the child, upon reaching majority, needs to affirm US citizenship or it is not regained.
But - since it is most likely that Zero never had US citizenship in the first place, it’s moot.
Until his real place and date of birth and parents are made public, it’s all a guessing game. Although a lot has been found out by researchers, the rock solid legal evidence has yet to be made public.