Motivated by the prevalence of "price protection guarantee", which helps to promote temporal fairness in dynamic pricing, we study the impact of such policy on the design of online learning algorithm for data-driven dynamic pricing with initially unknown customer demand. Under the price protection guarantee, a customer who purchased a product in the past can receive a refund from the seller during the so-called price protection period (typically defined as a certain time window after the purchase date) in case the seller decides to lower the price. We consider a setting where a firm sells a product over a horizon of T time steps. For this setting, we characterize how the value of M, the length of price protection period, can affect the optimal regret of the learning process. Our contributions can be summarized as follows: