In real-world applications, machine learning (ML) models need updates to adapt to evolving data. However, substantial changes due to updates, such as sudden drops in accuracy and inconsistencies in model behaviors, can undermine user trust. Prior backward compatibility research has mainly focused on maintaining the consistency of predictions for samples predicted correctly before the update. Recently, a new method called BCXR introduces the backward compatibility of explanations, which refers to the consistency of how ML models make predictions, measured by the importance of each feature during the prediction process. Nonetheless, BCXR is only applicable to differentiable models, limiting its usage in many applications where non-differentiable models, such as Gradient Boosting Decision Trees (GBDT), are preferred due to data characteristics and computational constraints. To address this limitation, we propose Linear Interpretable Backward-compatible Explanations (LIBE), which is applicable to GBDT as well as differentiable models. LIBE focuses on the backward compatibility of explanation through weighted linear regression, demonstrating that the differences between pre- and post-update explanations can be integrated into a differentiable loss function without requiring the models to be differentiable. Our experiments on GBDT show that LIBE effectively reduces explanation changes caused by retraining while maintaining accuracy.