If a background agent needs more direction, you resume it by passing its agent ID back to Claude. The agent retains the full context from its previous run, so you don't have to re-explain the task.
This is useful when an agent finishes a phase and needs direction for the next one, or when it reached a decision point. Instead of starting a new agent from scratch, you pick up where it left off.
I find the clearest pattern is to check the current output first, then tell Claude to continue with the specific agent ID so it knows which session to extend.