I don't think this counts as distillation. Distillation is when you use a teacher model to train a student model, but crucially, you have access to the entire probability distribution of the generated tokens, not just to the tokens themselves. That probability distribution increases tremendously the strength of the signal, so the training converges much faster. Claude does not provide these probabilities. So, Claude was used for synthetic training data generation, but not really for distillation.