I was at a store, and the cashier scanned my check and then handed it back to me. Is this normal?

The scan will capture the specific number on the check so that it can be identified on your statement. You can hold on to the check for your records, but don’t use it to make another payment, even to the same merchant, because your bank or credit union may reject it.

The retailer or other person must provide notice of this practice on a sign near where it accepts checks. 

You have some important additional protections when your check is turned into an electronic transaction by scanning it.