If you talking about food type items in pet inventory its common “problem”.
I notice if you keep various food (grass, meats, etc) in Your pet feeder, then gluttony pets can snatch some random food to their inventory.
My solution earlier for that was to fill pet invetory with 1 piece of simple item like pet skin to block their slot for food steal, or just remove various food from pet feeder.

Of course above example is for nothing if pet You mentioned steal other type items than food.