  We collect some observations about Legendrian links with non-vanishing
contact invariants, mostly concerning the non-loose realizations of links and
the addition of boundary-parallel half Giroux torsion. In particular, we show
that every null-homologous link with irreducible complement admits a non-loose
Legendrian realization with non-zero (at least) invariant $\text{EH}$ in
$\text{SFH}$, in some overtwisted contact structure (determined by its
gradings); for many links these come from Gabai's work, for others the
existence follows from the sutured interpretation of link Floer invariants. We
reveal that separating half Giroux torsion does not necessary cause Legendrian
invariants to vanish. Furthermore, we propose a conjectural characterization of
links with non-vanishing $\widehat{\mathfrak L}$ in $\widehat{\text{HFL}}$
among links with non-zero $\mathfrak L$ in $c\text{HFL}^-$.
