One of the suits was filed by the Republican Party of Pennsylvania to challenge a state supreme court decision that allowed mail-in ballots to be counted as long as they were postmarked by Election Day, Nov. 3, and were received by Nov. 6.
The state made the change to accommodate difficulties imposed by the COVID-19 pandemic and the move was upheld by Pennsylvania's top court.
The move to extend the deadline only resulted in about 10,000 ballots, which would not have changed Biden's victory in the state, since he won by 80,000 votes.
Alito, Gorsuch and Thomas said the case was worth hearing because it could affect future election disputes.
"That decision to rewrite the rules seems to have affected too few ballots to change the outcome of any federal election," Thomas wrote. "But that may not be the case in the future.
"These cases provide us with an ideal opportunity to address just what authority non-legislative officials have to set election rules, and to do so well before the next election cycle. The refusal to do so is unacceptable."
The Supreme Court also rejected two cases challenging Biden's victories in Pennsylvania and Wisconsin based on similar claims against mail-in ballots, as well as complaints filed by Trump allies in Michigan, Georgia and Arizona, which were all states carried by Biden.