Well, many cats will present prey they've caught to their owners and draw attention to it, and I've heard that this is because they're bringing "food to the family", i.e. those dumbasses who can't hunt for themselves
. Maybe the sponge is the closest thing that triggers that instinct. But if she had kittens, and they were taken from her early, I guess it could be something to do with carrying kittens around.
If you don't want her doing this I'd try first praising her, then taking the sponge and hiding it for a few days, and if she does it again when it reappears try not giving her attention and then hiding it for longer. I think she'll outgrow it.
Winter riding is much less about badassery and much more about bundle-uppery. - malkin
1995 Kona Cinder Cone commuterFrankenbike/Selle Italia SLR Lady Gel Flow
2008 white Nakamura Summit Custom mtb/Terry Falcon X
2000 Schwinn Fastback Comp road bike/Specialized Jett