Deep learning-based EEG classification is crucial for the automated detection of neurological disorders, improving diagnostic accuracy and enabling early intervention. However, the low signal-to-noise ratio of EEG signals limits model performance, making feature selection (FS) vital for optimizing representations learned by neural network encoders. Existing FS methods are seldom designed specifically for EEG diagnosis; many are architecture-dependent and lack interpretability, limiting their applicability. Moreover, most rely on single-iteration data, resulting in limited robustness to variability. To address these issues, we propose IEFS-GMB, an Information Entropy-based Feature Selection method guided by a Gradient Memory Bank. This approach constructs a dynamic memory bank storing historical gradients, computes feature importance via information entropy, and applies entropy-based weighting to select informative EEG features. Experiments on four public neurological disease datasets show that encoders enhanced with IEFS-GMB achieve accuracy improvements of 0.64% to 6.45% over baseline models. The method also outperforms four competing FS techniques and improves model interpretability, supporting its practical use in clinical settings.