The customer can refuse, but the restaurant can equally refuse to accept the check. So unless you are good at washing dishes, I'd do what they asked. Besides, it really has no bearing.
The check is payable to J's Restaurant. J's endorsed the check and negotiated the item by depositing it. If it comes back, the bank will take the $$ out of J's account. Then J's will have to take it to the local DA's office and try to explain why the customer's signature is on the bank of the check. That might be fun to watch.
I went to the same restaurant and wrote a check in red ink. They made me write a new one in blue ink because red ink ment that I was stopping payment on the check. (joke)