Agentic large language model systems increasingly automate tasks by retrieving URLs and calling external tools. We show that this workflow gives rise to implicit prompt injection: adversarial instructions embedded in automatically generated URL previews, including titles, metadata, and snippets, can introduce a system-level risk that we refer to as silent egress. Using a fully local and reproducible testbed, we demonstrate that a malicious web page can induce an agent to issue outbound requests that exfiltrate sensitive runtime context, even when the final response shown to the user appears harmless. In 480 experimental runs with a qwen2.5:7b-based agent, the attack succeeds with high probability (P (egress) =0.89), and 95% of successful attacks are not detected by output-based safety checks. We also introduce sharded exfiltration, where sensitive information is split across multiple requests to avoid detection. This strategy reduces single-request leakage metrics by 73% (Leak@1) and bypasses simple data loss prevention mechanisms. Our ablation results indicate that defenses applied at the prompt layer offer limited protection, while controls at the system and network layers, such as domain allowlisting and redirect-chain analysis, are considerably more effective. These findings suggest that network egress should be treated as a first-class security outcome in agentic LLM systems. We outline architectural directions, including provenance tracking and capability isolation, that go beyond prompt-level hardening.