My comments below reflect my opinion. The Fed hasn't yet issued anything finally definitive on stored value cards, although they tried several years back.
I believe these products fall within the definitions of Regulation E. But the financial institution responsible for compliance here is not your bank (you don't hold the account of the consumer, and you are not providing access to that account). It's the company that issues the cards and does the accounting that is the Reg. E financial institution here, and they must do the Reg. E statements, error resolution, initial disclosures, etc.
Now, if all of this is being done in your bank's name and the issuing company is acting as your contractor/agent, you're back in the Reg. E seat, but you'll rely on the contractor to take care of statements. You'll also have to rely on them to provide you with error resolution support. Perhaps this is why your bank's name and number are on the cards?
With your bank's name and number on the cards, you're setting up an expectation on the part of the cardholders that your bank is the "go to" party, even if a legal analysis determines that Reg. E won't apply to you.
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John S. Burnett
BankersOnline.com
Fighting for Compliance since 1976
Bankers' Threads User #8