  We respectfully reply to Wang et al.'s reply to our comment to their [JHEP
$\textbf{09}$ (2021) 053]. Some more subtleties and details are discussed for
hopefully better clarification and understanding, especially about the
conditions in Hilbert's finiteness theorem. We also disprove Wang et al.'s
incorrect assertion in their reply [arXiv:2110.13865 [hep-ph]] that there is an
isomorphism between ${\rm U}(n,\mathbb{C})$ and ${\rm GL}(n,\mathbb{C})$. We
give two proofs for our argument. One proof is in the context of Lie group for
arbitrary positive integer $n$, and the other proof is in the context of
abstract group for $n=3$ which can also be generalized to $n\geq 3$. In order
to better illustrate the intrinsic differences between a compact Lie group and
its complexification, we choose ${\rm SU}(n,\mathbb{C})$ and ${\rm
SL}(n,\mathbb{C})$ as a pair of examples and give two proofs for the generally
non-isomorphic relation between them. One proof is in the context of Lie group
for integers $n\geq 2$, and the other proof is in the context of abstract group
for $n=3$ which can again be generalized to $n\geq 3$.
