It's simple, really: the scammer calls your hotel room pretending to be from the front desk, and says there's a problem with your credit card so they need you to verify your credit card information.
Similar to "phishing" scams
If this scam were perpetrated by email rather than over the phone, it would be called a “phishing” scam. Phishers send out emails claiming to be from some agency – your bank, the IRS, your mobile phone company – basically anyone who might, presumably, have an actual need to know certain sensitive data about you.
Of course, those same people or organizations presumably already have this data, and don't need to ask you for it. The IRS already knows your Social Security number, and once you've checked in to a hotel room with your credit card, of course the hotel now has your credit card info.
So why would hotel staff call your room later to ask for this information? They won't – but scammers pretending to be them will.
Someone recently tried pulling this scam on guests at the Hampton Inn in Knoxville, Tennessee. WBIR reports that hotel manager Neal Smith intercepted one such call: “Someone called into the front desk asking to speak to Mr. Smith. They transferred it up to my room and the person claimed to be my front desk operator and asked for my credit card number.”
Of course, the scammers failed to fool their intended victim: “I politely informed them that that's not the case. I'm the general manager at this hotel.”
Hotels will know if your card is valid
Smith went on to point out that, on the off-chance there actually is some sort of problem with your credit card, the hotel will know that before you even finish checking in: “We'll know right when you check in that that card's not a valid card, and we'll ask you at that time to provide a different method of payment. There should be no reason someone is calling you in your room asking for sensitive information.”
Whether you're getting scammy phone calls in your own home or hotel room, or checking messages in your email inbox, always remember the anti-scam rule “Don't call me, I'll call you.” If you want to call the hotel front desk because you think there might be some problem with your payment card, go ahead and call them. But if someone claiming to be from the front desk calls you – don't believe it. You can call them, but they won't really call you. Only scammers will.