In the wild, big cats bury their hard-won meat to preserve its freshness, much like our ancestors would dig out caches in the permafrost to store food for longer.
This was to cover up any trace of their presence so that potential enemies couldn’t track them from their food remnants.
Cats are notoriously clean creatures. They spend so much of their time grooming themselves that it can’t come as a shock. But they extend this cleanliness into their “dens”, and, therefore, your home.
Pawing at their food is a half-hearted attempt at burying it. Not all cats have access to a garden or are let outside on the regular, so they have other ways of satisfying those primordial yearnings.