They must either take the cash or forgive the debt, no matter what the sign says. If they don't want cash they shouldn't have served you food until they got their preferred payment method, in which case you could just walk out without having eaten and owe them nothing. Since they decided to serve you, then you now owe them money, which you must be allowed to pay back in cash with US currency. This rule is written on the face of the currency itself.
