The male was eating.
He holds the gobbet of meat. Probably bird, although last week I saw he was munching on a small mammal, a baby rat or a mouse. (Photo through screen window.)
And then, on Monday evening, the female was eating a lizard!
I first became aware of Italian Wall Lizards because of a picture that circulated some years ago. It showed an American Kestrel flying to a nest in Manhattan and ladened with a lizard. There are native East Coast species of lizards (for example, Eastern Fence) but none are found in NYC any longer. Podarcis siculus ssp. campestris is an introduced species. A native of the Mediterranean region, they were first bought in for the pernicious pet trade and that perverse market of those who keep wild animals captive. The lizards escaped out in Long Island and for half a century they have expanded — often along rock-strewn railroad lines.
I saw my first in a cemetery in Queens. The rocky outcrop at the Native Garden at NYBG is a reliable place to see them. Last year, I saw some in Brooklyn.
And so now, obviously, have the kestrels.
This lizard is now being converted into falcon eggs.
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Backyard and Beyond 
You will start to notice a considerable number of fledgling House Sparrows when the kestrel chicks hatch. This is an evolutionary adaptation that provides the raptors with an easy and plentiful supply of meat. Later in the summer the diet is leaner but still sufficient. I have even seen kestrels eating dragonflies. Who knew they could catch them!