Get the bank’s phone number and call it directly for verification.
Generally, you should not provide personal information over the phone unless you have initiated the call.
Write to the bank, requesting that it stop the solicitations.
You can stop receiving unsolicited "preapproved" credit card offers by having your name removed from the credit bureau mailing lists. Call 1-888-5-OPT-OUT (567-8688).
You can also contact your present creditors and ask to be placed on their "Do Not Solicit List."