  In this note, by explaining two key methods that were employed in
\cite{Liu-21} and by giving some remarks, we show that the proof of Theorem 1.1
in \cite{Liu-21} is a rigorous proof based on theory of strongly continuous
semigroups and pseudodifferential operators. All remarks and comments to paper
\cite{Liu-21}, which were given by Matteo Capoferri, Leonid Friedlander,
Michael Levitin and Dmitri Vassiliev in \cite{CaFrLeVa-22}, are incorrect. The
so-called "numerical counter-examples" in \cite{CaFrLeVa-22} are useless
examples for the two-term asymptotics of the counting functions of the elastic
eigenvalues. Clearly, the conclusion and the proof of \cite{Liu-21} are
completely correct.
