If this is the biggest problem you have with your nanny- you are lucky- if she shows up on time every day- and takes good care of the kids -- I think you should be happy..
we had issues with our nanny and too mcuh tv watching... but overall she has watched my daughter for a year- my daughter has never been hurt- there is no damage to the house.. no items have been stolen...etc...
I do think you can tell your nanny that an item is for a specail occasion and to please leave it.. Like if you bought a cake or desert for a party you were going to- you could ask her to leave taht-- if she is mainly eating leftovers taht is really not an issue.. and it might be the quickest and easiest thing for her to eat while watching your child.. maybe she feeds him some of he leftover dinner and eats the rest... that way she doesnt have to cook anything while watching him..
get some yellow sticky notes and mark any items that you want her to save for you..
but really it is not a big problem.