The only way to even legitimately contest a state’s electoral votes is for someone in a position of legal authority IN THAT STATE to notify Congress of the fraud, malfeasance, etc. that questions the validity of the electoral votes that had been sent to Congress. Preferably, this would be done by a state legislature that also votes on a competing slate of electors and sends them to Congress.
Sadly, the only way Pence likely could have sent the dispute back to the states is if the GOP-led legislatures in those states, per their Constitutional power, sent their own certified slates of electoral votes to DC, creating dueling, certified slates of electors. However, the state GOPs created the alternate slates of electors, and I’m not sure that the parties themselves can officially certify diddly-daddly.
This fraud-riddled election occurred, and thanks to the weak-tea GOP, we will never know who really won, and we will have to live with the results.