Wherein The Bug and I spend the better part of a day searching for said item. Best we can figure, she left the cleaner sitting beside the back door, where she had been using it. Apparently I picked it up and put it in the rag bag where it lives? (Vague memory.)
THEN, or so we would have you believe, the cleaner leapt of its own accord from the rag bag into the nearby recycling can.
From there, it was unceremoniously dumped into the outside bin, where it was unearthed after an exhaustive indoor search (not to mention two less thorough looks into the big bin).
(Note from The Bug: you can't see it very well, but there is a stink bug on the counter in the last picture with the cleaner. Stink bugs are like cats. You don't want them on the counter. You tell them to stay off the counter. They go where they will.)