Dunno if James is referring to carbon slips precisely there, which I don't think are around anymore, as opposed to the copies (now done without carbon slips in between) of an imprint voucher.
Some places like the motels, for example Hotel Maria Bonita want to imprint card and ¨keep¨until you leave...for ¨deposit¨purposes. I know a lot of the car rental places do this.
Also not sure how to read the use of square quotes there, but that's a perfectly legitimate practice for the business, and a relatively common one here, still. The only ways to secure a deposit or guarantee legitimately on a card are to:
1. swipe the card and get a signature on the electronic voucher
2. enter the card info manually and get a signature on the electronic voucher
3. take an imprint of the card and get signature on the imprinted voucher
Since many clients have cards that won't scan properly anymore, method 1 may be out, and it can be difficult for businesses to go the route of receiving permission for method 2 (special applications, approvals and insurance are required). The only other way to properly secure a deposit or guarantee is to go with method 3, which anyway is always automatically supplied to every vendor by the banks as a backup in case the electronic system is down. So just because a merchant is following that system does not mean the merchant is up to something.