A check on another bank was presented to us for cash. Under the person's name on the check it states" FOR DEPOSIT ONLY". It is not an endorsement because it is not directed by the person to whom the check was made payable. How can the bank that this check is on police this? HOw would they know if the check was deposited or cashed? Anyone ever seen anything like this?

Are you sure its a check? I've seen direct deposit notices that look exactly like a check but have verbiage similar to "deposited into your account" or something to that effect.

The other bank can not police this. They would have no way of knowing how you handle the check on your end. However, I would probably still treat this as a restrictive endorsement and ask for the customer to deposit the check.