Extended reasoning has substantially improved multimodal large language models (MLLMs) on tasks requiring compositional and relational inference. However, multimodal grounding imposes a distinct requirement: reasoning must ultimately converge on a target-specific compact representation that supports precise localization. As reasoning trajectories grow longer, they often expand into broad scene narratives and peripheral relational details, which can dilute grounded perceptual evidence and lead to ambiguous or incorrect predictions. Motivated by the information bottleneck principle, we propose Think-Compress-Answer (TCA), a reinforcement learning framework that decomposes multimodal grounding into three phases: free-form reasoning, target-aware context compression, and answer generation conditioned on the compressed context. TCA is optimized through a multi-stage Group Relative Policy Optimization (GRPO) with progressive rewards that establish the structured output protocol, minimize reasoning-specific information while preserving target-relevant content, and directly improve localization accuracy. This staged design enables MLLMs to retain the benefits of extended reasoning while distilling it into the minimal context required for grounding. Experiments across six multimodal grounding benchmarks show that TCA attains substantial zero-shot performance gains, demonstrating the effectiveness of reasoning compression.

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