Multi-agent systems powered by large language models (LLMs) increasingly decompose tasks by passing natural-language relays among specialized agents. This creates a boundary-level privacy failure: a non-entitled internal agent can learn private context before any final-output guard or tool-action checker observes a violation. We introduce contextual-integrity mediation for inter-agent communication, a formulation in which each candidate relay is treated as a commit that must satisfy recipient entitlement, attribute minimization, and transmission conditions before delivery. We present CI-Relay, a runtime mediation layer that induces CI scopes from runtime-visible norms and relay metadata, packages candidate messages as CI-labeled envelopes, projects recipient-scoped views, propagates transmission constraints, and records auditable mediation traces. On relay traces converted from three CI benchmarks, unmediated relays leak internally in 52.2% of cases. Relative to a metadata-matched LLM Guard Relay that receives the same induced scope, CI-Relay reduces internal leakage from 12.4% to 1.8% and downstream leakage from 10.9% to 5.6%, while improving utility and reducing over-redaction. Gains hold across three live LLM backends; multi-hop, prompt-robustness, and ablation studies show that the gains arise from structured CI mediation rather than generic privacy prompting, guard rewriting, or final-output checking.