I'm aware that if a bank has a raffle that is restricted to its customers, it in fact has a lottery (and this violates federal law). Some claim that by opening up the raffle to noncustomers, there is no longer a requirement to pay to play, and therefore no longer a lottery.

What if we open up the raffle to noncustomers, but require a local receipt? A receipt would implicitly require the contestant to have "advanced credit" to another. Thus, it seems like we would be back within the definition of a lottery.

Does this seem objectionable?

(We would like to give away a scooter as the prize.)

Once upon a time, I did some research on this subject, but I don't seem to be able to put my hands on the information at the moment. However, if my memory serves me right, I think what you are considering would still be a violation because they have to make a purchase somewhere to participate in your raffle.
I think in general, you can only get around the rules and have a drawing if it is open to customers and noncustomers and there is nothing they have to do to participate (no required account, nothing to purchase, etc.)
Again, this is just my opinion based on memory, since I don't have the documentation in hand to refer you to.

You're going to run foul of the Illinois Raffles Act too, if you require them to give value to play.
http://www.ilga.gov/legislation/ilcs/ilcs3.asp?ActID=1400&ChapterID=25

230 ILCS 15 is the Raffles Act. Only a not for profit can get a license.