We investigate how large-scale cosmic filaments impact the quenching of galaxies within one virial radius of 324 simulated clusters from The Three Hundred project. We track cosmic filaments with the versatile, observation-friendly program DisPerSE and identify haloes hosting galaxies with VELOCIRaptor. We find that cluster galaxies close to filaments tend to be more star forming, bluer, and contain more cold gas than their counterparts further away from filaments. This effect is recovered at all stellar masses. This is in stark contrast with galaxies residing outside of clusters, where galaxies close to filaments show clear signs of density related pre-processing. We first show that the density contrast of filaments is reduced inside the intra-cluster medium. Moreover, examination of flows around and into cluster galaxies shows that the gas flows in intra-cluster filaments are colder and tend to stream along with galaxies in their midst, partially shielding them from strangulation by the hot, dense intra-cluster medium. This also preserves accretion on to satellites and limit ram pressure.