Tool-Integrated Reasoning (TIR) improves the problem-solving ability of Large Language Models (LLMs), but current TIR agents often invoke external tools even when internal reasoning is sufficient. This cognitive offloading increases latency and can expose the model to noisy tool feedback. We propose AdaTIR, a difficulty-aware policy optimization framework that applies efficiency pressure only when a task is estimated to be solvable under the current TIR policy. This encourages reasoning internalization on easier tasks while preserving tool access for harder ones. We further identify a sign-reversal failure in group-normalized RL: once rollouts in a group are mostly correct, an auxiliary tool-use penalty can dominate the correctness signal and assign negative advantages to correct but tool-heavy trajectories. AdaTIR addresses this with Clipped Advantage Shaping (CAS), which keeps efficiency as a bounded secondary signal. Across mathematical benchmarks, AdaTIR reduces average tool calls by up to 97.6% while maintaining or improving accuracy, and improves AIME 2024 accuracy by 4.8% when tool access is disabled. Additional results on search-based QA and mixed-tool settings indicate that the mechanism is not limited to Python-based math reasoning.