This work addresses the limitations of deep neural networks (DNNs) in generalizing beyond training data due to spurious correlations. Recent research has demonstrated that models trained with empirical risk minimization learn both core and spurious features, often upweighting spurious ones in the final classification, which can frequently lead to poor performance on minority groups. Deep Feature Reweighting alleviates this issue by retraining the model's last classification layer using a group-balanced held-out validation set. However, relying on spurious feature labels during training or validation limits practical application, as spurious features are not always known or costly to annotate. Our preliminary experiments reveal that ERM-trained models exhibit higher gradient norms on minority group samples in the hold-out dataset. Leveraging these insights, we propose an alternative approach called GradTune, which fine-tunes the last classification layer using high-gradient norm samples. Our results on four well-established benchmarks demonstrate that the proposed method can achieve competitive performance compared to existing methods without requiring group labels during training or validation.