There is not, nor was there ever, any mechanism or power in the Constitution or laws or congressional rules giving the Vice President this kind of authority to “send it back” nor any mechanism for the States to have a do-over after they already sent in their Electors. Period. To say otherwise is ignorance at best or lying at worst. But in both cases it is embarrassing this keeps being claimed. The only mechanism by which the Electors could be blocked is if they are rejected and not counted. Congress chose not to do this. The Vice President has no such unilateral authority - if a motion for him to rule on was brought during the proceedings, but that would subject to appeal and override by the full Congress...but even so, no such mechanism or authority to do what is proposed exists, nor ever existed. There is no power for the Vice President to send electors back. There is no power or mechanism for state legislatures to redo their Electoral votes after they have been submitted to Congress. That all has to come before the fact, and none of the legislatures chose to do so. That is simple reality.
Yes there is. The constitution requires the electors to be chosen by the legislature of each state, not the executive branch. If the legislatures did not certify the results, they don't meet constitutional muster.
The habit has been to allow employees of the executive branch to do it, but the Constitution says "legislature."