The Galactic foreground contamination in CMBR anisotropies, especially from the dust component, is not easily separable from the cosmological or extragalactic component. In this paper, some doubts will be raised concerning the validity of the methods used to date to remove Galactic dust emission in order to show that none of them achieves its goal. First, I review the recent bibliography on the topic and discuss critically the methods of foreground subtraction: the cross-correlation with templates, analysis assuming the spectral shape of the Galactic components, the "maximum entropy method", "internal linear combination", and "wavelet-based high resolution fitting of internal templates". Second, I analyse the galactic latitude dependence from WMAP data. The frequency dependence is discussed with the data in the available literature. The result is that all methods of subtracting the Galactic contamination are inaccurate. The galactic latitude dependence analysis or the frequency dependence of the anisotropies in the range 50-250 GHz put a constraint on the maximum Galactic contribution in the power spectrum to be less than a ~10% (68% C. L.) for a ~1 degree scale, and possibly higher for larger scales. The origin of most of the signal in the CMBR anisotropies is not Galactic. In any case, the subtraction of the Galaxy is not accurate enough to allow a "precision Cosmology"; other sources of contamination (extragalactic, solar system) are also present.