Remittance Status Verification Act of 2013 - Amends the Electronic Fund Transfer Act to require a remittance transfer provider, before initiating a transfer, to request from the sender of a remittance whose recipient is located in a country other than the United States proof of the sender's status under U.S. immigration laws.

Cites admissible documentation attesting to the sender's status, including a state-issued driver's license or federal passport.

Directs a remittance transfer provider to impose, upon any sender unable to provide such proof of status, a fine equal to 7% of the U.S. dollar amount to be transferred.

Requires submission to the Consumer Financial Protection Bureau (CFPB) of all fines imposed and collected by a remittance transfer provider in order to pay the administrative and enforcement costs of implementing this Act.

Requires the Comptroller General (GAO) to study the effects of the enactment of this Act.