Exploratory manipulation often turns an apparent failed attempt into the key evidence for what to do next. For example, a robot pulls a locked cabinet drawer, fails, and only succeeds after opening the lock. The failed pull reveals a latent precondition (the drawer is locked) that determines the minimal-success action chain (the fewest actions that complete the task), here [lock-open, drawer-pull]. Correctly reading this trace is therefore the prerequisite for recovering that chain. We formalize this setting as Exploratory Manipulation Trace QA (EMT-QA): given synchronized video and proprioception from an exploratory trace, predict the minimal-success action chain under the latent precondition revealed by the probe. However, even state-of-the-art VLMs and embodied multimodal LLMs misread this evidence: they do not reliably recover the chain from raw video, raw proprioception, or their combination. We introduce Closed-Loop Trace Distillation, a pipeline that uses a per-task coding agent to inspect labeled training traces and distill a one-line natural-language prompt over the trace, which we call the Distilled Reading Heuristic (DRH). At inference, no agent is invoked and no model weights are updated; a frozen VLM receives the raw trace plus the DRH as a prompt entry. Across three simulator and two real-robot tasks, the DRH improves chain accuracy by +0.38 to +0.47 over the best raw-modality baseline. The same DRH also serves as the sole specification for one-shot programmatic classifiers that match the prompted VLM.