It is well-known that neural networks can unintentionally memorize their training examples, causing privacy concerns. However, auditing memorization in large non-auto-regressive automatic speech recognition (ASR) models has been challenging due to the high compute cost of existing methods such as hardness calibration. In this work, we design a simple auditing method to measure memorization in large ASR models without the extra compute overhead. Concretely, we speed up randomly-generated utterances to create a mapping between vocal and text information that is difficult to learn from typical training examples. Hence, accurate predictions only for sped-up training examples can serve as clear evidence for memorization, and the corresponding accuracy can be used to measure memorization. Using the proposed method, we showcase memorization in the state-of-the-art ASR models. To mitigate memorization, we tried gradient clipping during training to bound the influence of any individual example on the final model. We empirically show that clipping each example's gradient can mitigate memorization for sped-up training examples with up to 16 repetitions in the training set. Furthermore, we show that in large-scale distributed training, clipping the average gradient on each compute core maintains neutral model quality and compute cost while providing strong privacy protection.