Semi-supervised learning for LiDAR semantic segmentation often suffers from error propagation and confirmation bias caused by noisy pseudo-labels. To tackle this chronic issue, we introduce RePL, a novel framework that enhances pseudo-label quality by identifying and correcting potential errors in pseudo-labels through masked reconstruction, along with a dedicated training strategy. We also provide a theoretical analysis demonstrating the condition under which the pseudo-label refinement is beneficial, and empirically confirm that the condition is mild and clearly met by RePL. Extensive evaluations on the nuScenes-lidarseg and SemanticKITTI datasets show that RePL improves pseudo-label quality a lot and, as a result, achieves the state of the art in LiDAR semantic segmentation.