Ordering A Gift Card Online Using A Debit Card: Is this proper verification procedure?

[Leslie J]

We ordered a gift card from Sears online last night. Early this morning, someone called claiming to be from Sears, and said that they were on a conference call with our bank, and needed a social security number to verify that we were actually the ones who ordered it, since it was for a somewhat high amount (and the order was placed using a debit card, not a credit card). My husband told her his social security number before I could stop him. When she asked for the amount of a recent deposit to our account for further verification, I got on the phone and terminated the call, but now I am worried. I called our bank and found out it was indeed our banker who was part of this conference call, but I still do not know for sure that the other party (who initiated the call) is really Sears. I've tried calling and emailing Sears, but they cannot tell me whether a call was placed here by anyone there at that specific time. Should I be worried then, and if so, what should we look out for now?