Backporting changes to stable releases is a critical yet high-stakes maintenance task. In practice, large-scale ecosystems like OpenStack rely on explicit governance rules for stable branches, where many repositories enforce that changes cannot be merged or released without an explicit backport-related vote (e.g., Backport-Candidate). However, identifying changes that are safe to backport remains largely manual, leading to significant decision latency and inconsistency. To alleviate this challenge, we present BackportCheck, a decision-support tool implemented as a Chrome extension for the Gerrit code review interface. BackportCheck is based on a Gradient Boosting model (XGBoost), trained on historical process data, combined with a Large Language Model (LLM) that generates concise, human-readable justifications for predicted backport decisions. We evaluate BackportCheck for both usefulness and usability across 3,422 OpenStack changes, achieving 81.31% accuracy while maintaining a mean end-to-end response time of 1.39 seconds, outperforming CodeBERT-based classifiers and standalone LLMs. BackportCheck is available via GitHub . A video demonstrating the tool usage is available on YouTube.