Reinforcement learning with verifiable rewards (RLVR) has become a dominant paradigm for improving the reasoning capabilities of large language models (LLMs). Recent tree-based methods such as TreeRPO extend flat trajectory sampling with tree-structured rollouts to obtain dense, step-level reward signals without a separate process reward model. However, not all trees are equally informative: trees where all leaves succeed, all leaves fail, or the policy already predicts the reward distribution contribute little to gradient updates, wasting compute. We introduce CATPO (Critique-Augmented Tree Policy Optimization), which diagnoses and addresses this waste at the tree level. CATPO first scores each tree via a tree informativeness score, F(T), combining leaf-outcome diversity with policy-reward decorrelation at zero extra compute. For dead-wrong trees where all branches fail, CATPO applies critique-guided healing: it locates the shallowest failure point, generates a natural-language critique, and grafts refined continuations to recover training signal. Finally, an informativeness-weighted loss scales each tree's gradient contribution by its normalized score, concentrating parameter updates on the most informative trees while preserving overall gradient magnitude. Experiments on Qwen2.5-Math-1.5B trained with the MATH dataset show that CATPO achieves 37.5% macro accuracy across four benchmarks (AIME24, MATH-500, OlympiadBench, and MinervaMath), improving over TreeRPO by 1.9% and GRPO by 4.8%.