Since those requirements are in the Constitution, this is a matter for the Courts, not the U.S. House of Representatives.
Article I Section 5 states that the House is the judge of its own qualifications. If they are honest, they would judge that the Georgia seat was filled unconstitutionally and vacate the seat.
A court cannot vacate a seat, as that is not an Article III power, since Article I already has the remedy.
The only play for Democrats is to force the states of Georgia and Tennessee to both declare that this woman was a primary resident of Georgia and not Tennessee. Otherwise, by the states' own declarations, she is unconstitutionally seated and Pelosi's oath of office would force her to do the constitutional thing remedy the situation.
That would be to vacate the seat and have Georgia call for a special election. To do otherwise would really hurt the Democrats because it would another very public display of one rule of law for Democrats and another rule of law for the rest of us.
-PJ