Grey squirrels can be legally trapped and killed for sport, pest control or consumption in the United States. There are no seasonal restrictions on trapping on private property when the squirrel is killed for consumption.
Regulations apply to squirrel hunting, and vary by state. A squirrel may be trapped on private property any time of year, but if it is captured and not consumed in the off-season for hunting, it must be immediately cremated or buried.
Squirrel meat was a staple of American meals up until the mid 1900's, when it fell out of popularity due to the rise of the modern grocery store.