Embedded AI agents on edge devices can learn as a federation and keep improving after deployment. Each agent collects new trajectories with the current policy, and the edge server aggregates them in later rounds. In such self-improving agent networks, deleting data is harder than a one-time model repair. The data to be deleted may have already shaped later retained trajectories, so retraining or model-side unlearning leaves an influence echo that returns as the network keeps learning. We propose Muting Unlearned Trajectories' Echoes (MUTE) for reliable deletion over edge networks. MUTE traces the echo from a lightweight ledger at the edge server, without moving raw trajectories off the devices. It erases the current residue with a forget-retain update, contains high-influence retained trajectories, and audits later behavior to schedule further erasure under the uplink budget and the response deadline. On LIBERO, MUTE keeps the regenerated share of forgotten behavior at or below 0.401 for every request type, against at least 0.466 for five recent methods.

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