The biases present in training datasets have been shown to affect models for sentence pair classification tasks such as natural language inference (NLI) and fact verification. While fine-tuning models on additional data has been used to mitigate them, a common issue is that of catastrophic forgetting of the original training dataset. In this paper, we show that elastic weight consolidation (EWC) allows fine-tuning of models to mitigate biases while being less susceptible to catastrophic forgetting. In our evaluation on fact verification and NLI stress tests, we show that fine-tuning with EWC dominates standard fine-tuning, yielding models with lower levels of forgetting on the original (biased) dataset for equivalent gains in accuracy on the fine-tuning (unbiased) dataset.