>>4568971 (lb) the case that guides this is
Powell v. McCormack, I haven't read the case but would like to. Basically it goes like this
House and Senate have the power to Judge the elections and their validity. If they have evidence to support the election was invalid for some reason or so form of corruption related to the election took place, they can exclude the incoming person. Otherwise they have to seat the person and call for a vote of 60 to expel the person.
Here is a quick read about it
https://www.govinfo.gov/content/pkg/GPO-HPREC-DESCHLERS-V2/pdf/GPO-HPREC-DESCHLERS-V2-2-4-3.pdf