As Dude said, there is Reg DD & Q - IF - the gift you are giving is related to an account opening = Bonus, Interst, etc.
If I read between the lines of your question, I think you are asking if there is any concern with giving a gift to your "Best" existing customers.
For example, a set of Kitchen Knives / nice Leather Portfolio / etc to customers who keep over $300k on deposit, or borrower over $1.5MM etc.
IMO - this is not a problem, just keep it quiet and under the radar or you will have other customer who think they are a "Good Customer" wanting to know why they didn't get what Jane Doe got. And don't put your bank logo on it or then "technically" you should include FDIC Insured.
_________________________
My opinions are just that, and might be worth what you paid for them.