Adsorbates on graphene can create resonances that lead to:efficient electron scattering and strongly affect the electronic conductivity. Therefore, a proper description of these resonances is important to gain a good insight into their effect on conductivity. The characteristics of the resonance and in particular its T-matrix depend on the adsorbate itself but also on the electronic structure of graphene. Here the authors show that a proper tight-binding model of graphene which includes hopping beyond the nearest-neighbor leads to sizable modifications of the scattering properties with respect to the mostly used nearest neighbor hopping model. the authors compare results obtained with hopping beyond the nearest-neighbor to those of the recent work (2013 Phys. Rev. Lett. 113146601). The authors conclude that the universal properties discussed in the recent work are unchanged but that a detailed comparison with experiments req!lires a sufficiently precise tight-binding model of the graphene layer.