If we have a bank customer sending a foreign wire and the recipient bank does not have a GIIN is the bank required to apply a 30%withholding?

A withholding agent that is not related to a documented beneficial owner or payee is not required to withhold on a withholdable payment made if the withholding agent lacks control, custody, or knowledge of the payment. For additional information, refer to IRS Reg. §1.1471-2(a)(4)(i)(A). A sit down with your tax attorney might also be in order if you need further clarification on the terms "control, custody, or knowledge of the payment".