You can find the filing at this link.
As expected the Purcell Principle plays a major role in the argument here, the idea that courts should not make last minute changes in election rules because doing so could confuse voters and election administrators.
In this case, since we are so close to the actual election and there will have to be time for a response to this pleading, and for the Justices to decide the case. it may well be the the Principle would cut against the Supreme Court reversing at this time. (And I’ve written that the Principle itself should be just one factor; very important also are the merits of the parties position, and here the dangerousness of voting in person due to Covid-19 surely will weigh on the Justices.)