The twelve jurors are busy writing on their slates, and Alice asks what they are doing. She wonders why they are writing before the trial has even started. The Gryphon explains that the jurors are writing down their names to remember them throughout the trial, indicating they are preparing in advance for the proceedings.
The twelve jurors were all writing very busily on the slates. What are they doing? Alice whispered to the Gryphon. They can't have anything to put down yet, before the trial's begun. They're putting down their names, the Gryphon whispered in reply, for fear they should forget them before the end of the trial.