The mitigation of clutter is an important research branch in Integrated Sensing and Communication (ISAC), one of the emerging technologies of future cellular networks. In this work, we extend our previously introduced method Clutter Removal with Acquisitions Under Phase Noise (CRAP) by means to track clutter over time. This is necessary in scenarios that require high reliability but can change dynamically, like safety applications in factory floors. To that end, exponential smoothing is leveraged to process new measurements and previous clutter information in a unique matrix using the singular value decomposition, allowing adaptation to changing environments in an efficient way.We further propose a singular value threshold based on the Marchenko-Pastur distribution to select the meaningful clutter components. Results from both simulations and measurements show that continuously updating the clutter components with new acquisitions according to our proposed algorithm Smoothed CRAP (SCRAP) enables coping with dynamic clutter environments and facilitates the detection of sensing targets.