In recent years, emerging applications, such as diffuse optical imaging and spectroscopy (e.g., functional brain imaging and optical mammography), in which a wide dynamic range is crucial, have turned the interest towards Single-Photon Avalanche Diode (SPAD). In these fields, the use of a fast-gated SPAD has proven to be a successful technique to increase the measurement sensitivity of different orders of magnitude. However, an unknown background noise has been observed at high illumination during the gate-OFF time, thus setting a limit to the maximum increase of the dynamic range. In this paper we describe this noise in thin-junction silicon single-photon avalanche diode when a large amount of photons reaches the gated detector during the OFF time preceding the enabling time. This memory effect increases the background noise with respect to primary dark count rate similarly to a classical afterpulsing process, but differently it is not related to a previous avalanche ignition in the detector. We discovered that memory effect increases linearly with the power of light impinging on the detector and it has an exponential trend with time constants far different from those of afterpulsing and independently of the bias voltage applied to the junction. For these reasons, the memory effect is not due to the same trapping states of afterpulsing and must be described as a different process.