Realistically speaking, there is not a means for expungement or removal.
If the FBI processes your fingerprints, including for a job background check, you can anticipate that they'll be included in the FBI’s Next Generation Identification (NGI) database, which includes fingerprints taken for both civil and criminal reasons. Once included, unless the agency that required your fingerprints to be collected asks that the FBI remove them from the database, you would need a federal court order to get them removed -- and there's no clear mechanism to seek or obtain such an order.

