You don't really "file for return of backup withholding." What you do is prepare your income tax return, an income tax return that includes the sale of the stock. Included in that income tax return is the tax withheld by the trust company. If all the taxes you paid - withholding from your paycheck, estimated quarterly taxes, the backup withhold by the trust company, etc. - amounts to more than your tax liability then you will get a refund.
There's no "exemption" from backup withholding because you inherited stock. The trust company sent you a Form W-9 requesting certain information. A section of that form provides for your certification that you are not subject to backup withholding. If you failed to return this form or filled it out improperly, the trust company can subject payments to backup withholding.