What exactly could he have done? Essentially, what happened was that the Court took a case which circumstances had already rendered moot before it was heard. Nobody could argue that the decision was unfair for the winner, because he "won"; nobody could argue that the decision was unfair for the "loser" because he didn't really lose anything. Since nobody could really dispute the outcome, nobody could really protest that the court had no legitimate authority to make the decision in the first place.
There is nothing in the Constitution that gives the judiciary the power to review laws passed by congress and declare them unconstitutional. Marshall was motivated by politics. He was a Federalist while Jefferson and Madison were "Democratic-Republicans." Marbury, like Marshall, was a Federalist.
Marshall wanted to embarrass and rebuke Jefferson and Madison, so he created out of whole cloth the notion of "judicial review," grabbing for the court the power to rule acts of congress unconstitutional. That was the first violation of the separation of powers in our history.
Jefferson (and congress, for that matter; it was filled with Jeffersonians at the time) should have been true to the founding constitutional principles and told the court it had no standing to even rule on the Marbury matter. Jefferson should have made the case publically for rejecting "judicial review" of acts of congress, because such review is not in the constitutional powers granted the court. We have had an increasingly runaway judiciary ever since.