My cats (3) all leave that bit under the table for us or worse. I have to confess that I found the galbladder in the babies mouth, he was chomping away happily on it!!
We also get complete sets of rabbit's intestines, I don't know how they manage to skin them so skilfully. They are amazing, but revolting when you step in them in the dark in the laundry room if I go down for a glass of water in the night from the cooler!!