X-ray computed tomography (CT) is an invaluable imaging technique for non-invasive medical diagnosis. However, for soft tissue in the human body the difference in attenuation is inherently small. Grating-based X-ray phase-contrast is a relatively novel imaging method which detects additional interaction mechanisms between photons and matter, namely refraction and small-angle scattering, to generate additional images with different contrast. The experimental setup involves a Talbot-Lau interferometer whose susceptibility to mechanical vibrations hindered acquisition schemes suitable for clinical routine in the past. We present a processing pipeline to identify spatially and temporally variable fluctuations occurring in an interferometer installed on a continuously rotating clinical CT gantry. The correlations of the vibrations in the modular grating setup are exploited to identify a small number of relevant fluctuation modes, allowing for a sample reconstruction free of vibration artifacts.