More than likely you'll only get a polite nod of the head and an evasive answer. After all, he's not looking for a fight. Do not hestitate, however, as you would with any customer, to tell him that you hoped he enjoyed his meal. In a phrase - don't try to sell the critic something. The quality of the cuisine, the ambiance, the price-value ratio and the service at your establishment are what are important.
Bribery is offensive, flattery is demeaning, and begging is pathetic.
The quality restaurant needs none of these to receive favorable reviews. Good reviews give business an immediate boost. Keeping this edict in mind, the best reaction to most reviews, good, bad or indifferent, is nearly always a minimal reaction. In the event of a favorable review, no reaction is necessary. With regard to a negative review, most thinking people agree that the most elegant response is no response at all.