  This is a note on a recent paper of De Simoi-Kaloshin-Wei \cite{DKW}. We show
that using their results combined with wave trace invariants of
Guillemin-Melrose and the heat trace invariants of Zayed for the Laplacian with
Robin boundary conditions, one can extend the Dirichlet/Neumann spectral
rigidity results of \cite{DKW} to the case of Robin boundary conditions. We
will consider the same generic subset as in \cite{DKW} of smooth strictly
convex $\mathbb Z_2$-symmetric planar domains sufficiently close to a circle,
however we pair them with arbitrary $\mathbb Z_2$-symmetric smooth Robin
functions on the boundary and of course allow deformations of Robin functions
as well.
