Final answer:
If a client's credit card is declined at the reception desk, the receptionist should inform the client about the decline and ask if they have an alternative payment method.
Step-by-step explanation:
If a client's credit card is declined at the reception desk, the most appropriate next step is for the receptionist to politely inform the client about the decline and ask if they have an alternative payment method. The receptionist can also suggest that the client contacts their bank or credit card company to identify and resolve the issue. Additionally, the client can be offered the option to pay with cash or a different credit card, if available.