Loretta E. Lynch, the United States attorney for New York’s Eastern District and President Obama’s nominee for attorney general, signed off on Tuesday to a settlement that would return $447,000 seized from a family-run Long Island business under a controversial area of federal law known as civil asset forfeiture. The business, Bi-County Distributors, was initially targeted because of a pattern of cash deposits under $10,000, but its owners, the Hirsch family, argued that the deposits were legitimate and, though more than two years passed after the money was seized, no criminal charges were filed. Lawyers from the Institute for Justice filed a motion demanding the return of the money. In the resulting settlement, neither side in the case admitted wrongdoing. Last Friday, the outgoing Attorney General, Eric H. Holder Jr., announced a policy change to rein in federal participation in civil asset forfeiture.