  The recently discovered structural reconstruction in the cuprate superlattice
(SrCuO$_2$)$_n$/(SrTiO$_3$)$_2$ has been investigated across the critical value
of $n=5$ using resonant inelastic x-ray scattering (RIXS). We find that at the
critical value of $n$, the cuprate layer remains largely in the bulk-like
two-dimensional structure with a minority of Cu plaquettes being reconstructed.
The partial reconstruction leads to quenching of the magnons starting at the
$\Gamma$-point due to the minority plaquettes acting as scattering points.
Although comparable in relative abundance, the doped charge impurities in
electron-doped cuprate superconductors do not show this quenching of magnetic
excitations.
