Methods addressing spurious correlations such as Just Train Twice (JTT, arXiv:2107.09044v2) involve reweighting a subset of the training set to maximize the worst-group accuracy. However, the reweighted set of examples may potentially contain unlearnable examples that hamper the model's learning. We propose mitigating this by detecting outliers to the training set and removing them before reweighting. Our experiments show that our method achieves competitive or better accuracy compared with JTT and can detect and remove annotation errors in the subset being reweighted in JTT.