That is the problem with this whole issue - who has standing? Cruz can't do it - who would he sue? A voter can't do it - no standing. Perhaps the only one who can do it is another candidate. But then you get to the question of whether the court will hear the matter even if the plaintiff has standing if they do not consider the issue "ripe". They may decide that no injury has occurred unless and until Cruz wins the nomination - if he doesn't win, the issue is moot. The court does not pre-emptively rule on POTENTIAL injuries, unless the likelihood that the injury cannot be remedied afterward is extremely high.
I have read that there is no basis for a lawsuit unless Cruz is actually elected President. In that case, I doubt the courts would intervene and reverse the will of the people.
Congress could probably do something about it, but it’s likely one or both Houses will remain in GOP hands, so that won’t go anywhere.
Trump’s just blowing smoke.
AS long as Trump has spent money campaigning against Cruz, he has been injured by Cruz’ ineligibility, if Cruz is ineligible. Trump is having to spend money to run against a candidate who is potentially ineligible - that makes standing.