I have had a similar situation occur to me as well. Close-the-barn-door-after-the-horse-got-out advice notwithstanding
, I've had good luck just knocking the loose zinc around with a probe. If it fell off the threaded plug, it's like that it's pretty broken down and will crumble without too much trouble. Be careful not to cause any collateral damage as you knock it about. And flush as the unit well so that you get as much of the debris out the zinc-hole as possible.