In the era of foundational image segmentation models, there is a pressing need to leverage the outputs of these models and enhance the boundary accuracy of domain-specific segmentation results using lightweight post-processing techniques. Numerous existing boundary refinement approaches neglect the significance of incorporating diverse contextual scopes and global knowledge, resulting in restricted adaptability to different coarse segmentation errors. Moreover, the prevailing models are often lacking in lightweight design. To address these challenges, we propose a novel framework called Multi-Range Context Interaction (MRCI) that aims to refine the boundaries of predicted masks by incorporating comprehensive context knowledge while maintaining computational efficiency. Our approach utilizes a multi-range context-aware strategy to extract more informative local features and incorporates global knowledge prompts to guide the boundary refinement process. Experimental results on the widely used Cityscapes, ADE20K and satellite remote sensing dataset SpaceNet demonstrate the effectiveness of our approach, achieving top-tier Average Precision (AP) and mean IoU among the current state-of-the-art boundary refinement models while utilizing only 4M parameters. The source code will be available.