An elderly friend of mine fell for this. Fortunately I was in time to stop the scam in its tracks by calling the credit card's customer service number. They immediately cancelled the card, put the spurious charges "In Dispute" and issued a new one with her points transferred to it. Then the operator connected me to their fraud department, who instructed me to write "Refused" on all future mailings and send them back. From the tone of the conversation it is not unusual at all for this sort of thing to happen, and there is a process for dealing with it: cancel the card, dispute the bad charges, and write to the jewelry company canceling everything. Keep a copy of that letter and send it certified mail.
You must cancel the credit card and report the problem to their fraud people. The jewelry company is never ever going to cancel your order or remove any charges or stop sending you unwanted items.
MOST IMPORTANT: The postings indicate that DEBIT Card numbers have been used to drain victims' bank accounts in amounts up to $4000.00. I really learned something from that: Never use a debit card to order anything over the phone, the internet or by mail!
Another point is it is very difficult for a housebound senior citizen to "keep a copy and send it certified mail". How, without a copy machine and a way to get to the post office?
In addition to the rest of this time-consuming hassle, my elderly friend is now receiving a deluge of offers of "Free prizes" "Free Gifts, no purchase necessary", "Just Send In The Card and Receive Free Offers". I think the best way to deal with those is to write "Deceased" on them and send them back. I hope it is effective.