  Nuclear symmetry energy is a fundamental quantity currently under intense
investigation in both nuclear physics and astrophysics. The {\it softness} or
{\it stiffness} of symmetry energy is still under debate and the extraction of
symmetry energy from neutron skin thickness $R_{\rm skin}$ remains a challenge.
Parity-violating measurements PREX and CREX provide important opportunities for
constraining $R_{\rm skin}$ in $^{208}$Pb and $^{48}$Ca. We investigate the
occurrence of $\alpha$-cluster at the surface of nuclei and its impact on the
extraction of symmetry energy from $R_{\rm skin}$. Our result indicates that
the $\alpha$-clustering probability in $^{208}$Pb is small and the extracted
density slope of symmetry energy $L$ is almost unaffected. In contrast, the
$\alpha$-clustering probability in $^{48}$Ca is sizeable and the corresponding
correction to $L$ should be taken into account. This correction progressively
increases with the $\alpha$-clustering probability, leading to a modification
of the $L$-$R_{\rm skin}$ correlation, a fact may have important implications
in constraining nuclear symmetry energy.
