dopant atoms also explained the origin of the dominant so-called ${\mathbf{q}}_1$ peak in the Fourier transformed scanning tunneling spectroscopy (FTSTS) data,[@nunner2; @mcelroyFTSTS] and the recently observed pair density wave driven by the structural supermodulation.[@slezak; @andersenslezak] In addition, it predicted the existence of islands with finite gap above T$_c$, as recently observed by Gomes [*et al.*]{}[@gomes] Such islands lead naturally to broadened thermodynamic transitions although this point remains controversial at present.[@andersen06; @loram]

Here, we show that within the modulated pairing scenario, the absence of Ni resonances in large-gap regions arises naturally when one properly includes the nano-scale inhomogeneity of the superconducting order parameter. This occurs because in-gap impurity resonances in a $d$-wave superconductor generically borrow their weight from the coherence peaks. In the large-gap regions, these peaks are broad and weak, so they overlap and swamp the weaker resonances located away from the Fermi level. In the small-gap regions, on the other hand, the structures normally referred to as coherence peaks are actually Andreev resonant states of the suppressed order parameter,[@nunner1; @acfang] and their height/width is significantly larger/smaller than in the pure homogeneous case. Thus in the small-gap regions the impurity resonances are well-defined due to their smaller overlap with the 