I'm no lawfag but it appears that the Flynn Judge is asking for help by the way of new information. Any lawyer licensed in the court's jurisdiction can file one. He's shouting for help (additional information pertaining to…) because otherwise he has to dismiss the case.
There's also the possibility of lawyers arguing over validity of a brief. This points to Q's mention of trying to extend the process.
https://www.law.cornell.edu/rules/supct/rule_37