We have a red and a red-grey squirrel in our area, with both of them rather frequently seen on the trees in the surrounding gardens... and the red-grey squirrel also in our garden. It not only tries to hide nuts there in the autumn, it also sometimes visits the compost heap, as you can see in this slightly blurry and also not very good photo:
The reason for this is an old, bleached bone lying on top of the heap. The squirrel goes there to gnaw on the bone (you can clearly see the tooth marks) - we think it might be for the calcium. We had a bone on top of the heap a while ago, by chance, and realised that it was a squirrel snack, so when one re-appeared in the compost (after being buried for a bit) I pulled it out and moved it up top.
Where it was almost instantly appreciated.