Coherent fiber bundles are widely used for endoscopy, but conventional approaches require distal optics to form an object image and acquire pixelated information owing to the geometry of the fiber cores. Recently, holographic recording of a reflection matrix enables a bare fiber bundle to perform pixelation-free microscopic imaging as well as allows a flexible mode operation, because the random core-to-core phase retardations due to any fiber bending and twisting could be removed in situ from the recorded matrix. Despite its flexibility, the method is not suitable for a moving object because the fiber probe should remain stationary during the matrix recording to avoid the alteration of the phase retardations. Here, we acquire a reflection matrix of a Fourier holographic endoscope equipped with a fiber bundle and explore the effect of fiber bending on the recorded matrix. By removing the motion effect, we develop a method that can resolve the perturbation of the reflection matrix caused by a continuously moving fiber bundle. Thus, we demonstrate high-resolution endoscopic imaging through a fiber bundle, even when the fiber probe changes its shape along with the moving objects. The proposed method can be used for minimally invasive monitoring of behaving animals.