The quality of astrophysical images produced by means of the Generalised Least Square (GLS) approach may be degraded by the presence of artificial structures, obviously not present in the sky. This problem affects in different degrees all images produced by the instruments onboard the European Space Agency (ESA) Herschel satellite. In this paper we analyse these artifacts and introduce a method to remove them. The method is based on a post-processing of GLS image that estimates and removes the artifacts subtracting them from the original image. We find that the only drawback of this method is a slight increase of the background noise which, however, can be mitigated by detecting the artifacts and by performing the subtraction only where they are detected. The efficiency of the approach is demonstrated and quantified using simulated and real data.