A better question is what would happen if it were a tie, but an elector went rogue and voted against the wishes of his state to make it 270-268?
How could this be challenged?
It really couldn't.
21 states don't even have laws compelling their electors to vote for a pledged candidate, so if the hypothetical scenario you've presented were to entail an elector from one such state, then their vote would be valid, & whomever they were the 270th electoral vote for would be President-elect.
Now, some of the other 29 states plus D.C. do have laws to penalize faithless electors, although these have never been enforced (& in lieu of penalizing a faithless elector, some states, such as Michigan & Minnesota (the latter of which invoked this law for the first time in 2016 when an elector pledged to Clinton attempted to vote for Bernie Sanders instead), specify that the faithless elector's vote is void & that a replacement elector will vote for the candidate whom the electors' party supports).
And while the Supreme Court has confirmed the constitutionality of state
pledge laws (ruling that states have the right to require electors to
pledge to vote for the candidate whom their party supports, & the right to remove potential electors who refuse to
pledge prior to the election), the ruling only held that requiring a
pledge, not a vote, was constitutional, & even went so far as to state that such promises of candidates for the Electoral College are legally unenforceable b/c they're violative of an
assumed constitutional freedom of the elector under the Constitution, Art. II, § 1, to vote as he [or she] may choose in the Electoral College.
Crucially, what this means is that, while the Court has never ruled on the constitutionality of state laws explicitly punishing or replacing electors for actually casting a faithless vote, or refusing to count said votes, it is generally believed that a state law that would thwart a federal elector's discretion at an extraordinary time when it reasonably must be exercised (such as a tied election, perhaps) would clearly violate Article II, as well as the 12th Amendment.
So, if the election were to be tied after Election Day, but then an elector voted for the other party's candidate rather than the candidate for whom they had pledged to vote, thus making it 270-268 & ensuring that the other party's candidate will be President, it really couldn't be challenged (successfully, anyway), due to the fact that it is implicit under the Constitution that electors are technically free agents who are free to exercise an independent & nonpartisan judgment as to the candidates best qualified for the nation's highest office.
