It does have this authority, explicitly under the Constitution. Democrats have used this authority in the past to overturn close certified election results they did not like.
There is absolutely nothing that can be done about it other than protest. It is 100% legal.
Do they already know what is on these 6500 rejected ballots, or are they still sealed?
Seems offhand that there would be two different Constitutional provisions in conflict: the provision in Article I giving each house the power to judge the qualifications of its members and the provision in the 17th Amemdment stating that Senators shall be elected by the people of their state.
The Supreme Court ruled otherwise in the case of Adam Clayton Powell.