  We discuss cosmic domain walls described by a tension red-shifting with the
expansion of the Universe. These melting domain walls emit gravitational waves
with the low-frequency spectral shape $\Omega_{gw}\propto f^{2}$ corresponding
to the spectral index $\gamma=3$ favoured by the recent NANOGrav 15 yrs data.
We discuss a concrete high-energy physics scenario leading to such a melting
domain wall network in the early Universe. This scenario involves a feebly
coupled scalar field, which can serve as a promising dark matter candidate. We
identify parameters of the model matching the gravitational wave
characteristics observed in the NANOGrav data. The dark matter mass is pushed
to the ultra-light range below $10^{-11}-10^{-12}\,\text{eV}$ which is
accessible through planned observations thanks to the effects of superradiance
of rotating black holes.
