We have 2 mogs, both from Cats Protection, Oliver Sprout, that we've had for about 6 years, and Minnie, who has been here for a year or more (hopeless on dates!)
I'm utterly convinced that Minnie was a scullery maid in a previous life!
She will "steal" washing up sponges, those steel scrubbing things, the odd rubber glove and the occasional dish cloth.
I got fed up with having to get out a new sponge every time she stole one, so I set up a small box in the hall where I put sponges that were past their best so she could "steal" them at her leisure, so to speak!
We find them all over the house, but mainly in my husband's side of the bed (she adores him, and I think she leaves them there as an "offering"!)
She's weird, but we've learnt to accept it!