We have precedent on four occasions for challenging an election.
1) 1796, There was a flawed, illegally prepared slate of electors (I forget if it was from GA or NH). John Adams sat down when he got to reading that “vote” from the slate of electors to entertain a challenge from the floor. Jefferson instructed his supporters NOT to challenge. Adams became pres.
2) 1800 same thing, but with Jefferson counting, but he didn’t even sit down when he came to the irregular state (again, it was either GA or NH) slate. He just blew right past it. TJ became pres.
3) In 1876, three states’ electors were viewed as illegitimate. It took a join commission of Congress to settle this with the Compromise of 1877.
4) In 1960, Hawaii’s governor quickly sent in a slate of electors for, as I recall, Nixon. But the legislature sent in a second slate for JFK. Then a recount showed JFK won Hawaii, so the state (can’t recall if it was gov or leg) sent in a THIRD slate of electors for JFK. Richard Nixon accepted and read the slate from the third, recounted, slate.
Clearly a veep has the authority to a) recognize a challenge from the floor, upon which he refers the slates to the House and Senate meeting in separate sessions; b) ignore any discrepancies (Pence’s route); c) reject any slates that, in estimation were fraudulent; or d) refer the entire matter to Congress (the 1876 solution).
The 1960 case is the most instructive. It is important to note that all the legal and procedural maneuvering related to the three slates of electors took place before the joint session of Congress in January 1961. The reason that particular case is not all that relevant to 2020 was that Hawaii actually certified multiple slates of electors. In 2020, there wasn't a single state that submitted more than one slate of electors to Congress after the Electoral College certification in mid-December (December 14th, I believe).