Scam?

[PM_Mama00]

So I'm a lil confused. This number from Florida has been calling me everyday for almost a month. I answered the first time and figured it was a telemarketer so I said "Phyllis isn't here... blah blah". They have kept calling so I've been ignoring. Finally i answer and it's this woman and she's telling me that she wants to send me information about their company and even if I'm not interested I can still keep the free gifts. It was like Star something. Not sure. Anyways so she verifies my address and my name... she already had this information. Then she asks me what bank I use and I say National City and she asks if I started my account here in Southgate and I say yes. Then she asks for my checking account number just to verify that my account is active. I told her that I don't feel comfortable giving that out and she said that whenever I write checks people see the number at the bottom of the check... I guess she was trying to assuer me that it's safe? So she reads off my bank routing number and it's correct but I tell her that I don't have my checkbook on me so I'm not sure what the numbers are or if they are correct and I keep telling her that I don't want to give my number out over the phone. And she asks me again about the routing number and finally I'm like "I DON"T HAVE MY CHECKBOOK ON ME". I could tell she was getting frustrated when she was tryin gto explain how people see the checking account number all the time when I write checks but I'm thinking "yeah asshole stores see my credit card number too but I'm nto giving that out". After I finally repeated that I didn't have my checkbook on me she hung up on me.

The number is 727-471-1416 and it's Florida based. Is there somewhere I can look or try to find out if this is a scam? If I've never written a check to this place how would they have my routing number? Do I need to cancel this account and start a new one with new numbers?