And it appears they have the authority to do just that:
The House Democratic investigations could pave the way for a new election in the district, even if the court orders the board of elections to certify Harris as the winner instead of the board ordering a re-vote itself. The House Administration Committee, now controlled by Democrats, has the authority to call for another election after investigating the 2018 results.
Rep. Marcia Fudge (D-Ohio), who is slated to chair an election-focused subcommittee of the House Administration Committee, told POLITICO that the House will intervene if the North Carolina court ordered the election certified for Harris before the state investigation has concluded. Any House member could object to seating Harris and block him, triggering an investigation by Fudge's committee.
It might seem like a trivial detail, but you'll notice from the headline above I didn't say, "...court tries to certify Harris." Because it does not have that authority. It does, however, have the authority to "direct" the NC BoE to certify Harris, via Writ of Mandamus. But Congress itself has the final say, apparently:
If Harris does manage to get certified as the election winner, McCready — who initially conceded the race but has since withdrawn the concession and started preparations for a new election — could contest the certification, triggering a provision in the federal election law that would prompt an investigation by the Administration Committee.
Even if McCready didn’t contest the result and Harris showed up to Congress with certification papers demanding to be seated, any member could object by presenting a resolution, which would force a floor vote. At that point, Democrats expect they would have enough votes to send the matter to the House Administration Committee for investigation.
It's safe to say the NC GOP should avoid that particular scenario like the plague. Because that investigation, which will be front-page news across the country, will expose the fact they were aware of these shenanigans (at least) earlier in the year when Pittenger complained about them, if not actually before that time period. And their payments to Red Dome Group will also receive wider exposure.
And if you're harboring any fears Dallas and Robin might try to seek aid and comfort from the Conservative U.S. Supreme Court, not even that body would dare to challenge the U.S. Constitution:
1: Each House shall be the Judge of the Elections, Returns and Qualifications of its own Members, and a Majority of each shall constitute a Quorum to do Business; but a smaller Number may adjourn from day to day, and may be authorized to compel the Attendance of absent Members, in such Manner, and under such Penalties as each House may provide.
Bolding mine, because that is not ambiguous, at all.