Can we market a new deposit product that is available only for new deposit dollars to the bank? Suggestions on how to properly disclose?

Can you? Sure. Just make sure you carefully disclose what you mean by new money. You need to judge the blowback from your existing customers and make sure you make no exceptions due to the new fair banking initiatives.

https://account.chase.com/consumer/...YYw5Y90RbkaAk7iEALw_wcB&gclsrc=aw.ds

One example, you can find others. "Offer not available to existing Chase checking customers, or those whose accounts have been closed within 90 days or closed with a negative balance within the last 3 years..."