I've recently done some research and spoke with TSA regarding this.
Unfortunately, contrary to common belief, the federal law doesn't specifically state that the fee must be refunded to the passenger, or in what form. Only that if not refunded, the carrier must still remit the fee to the TSA.
A 2002 letter from the Acting Director of Revenue for TSA in response to a request seeking clarification of a carrier's responsibilities regarding refunds seems to indicate that carriers must grant a full refund upon request, but that specific direction was never added to subsequent law.
Anyone wishing to use that letter as reference can find it here (pdf):
http://www.benedelman.org/travel/randall_fiertz-21nov2002.pdf
The full docket is here:
https://www.regulations.gov/docket?D=TSA-2001-11120