The indecomposability conjecture for a Lagrangian concordance from the trefoil

Let $W\subset J^1(S^1)$ be the Legendrian Whitehead double pattern, let $U$ be the standard Legendrian unknot, and let $\Lambda$ be the Legendrian $\overline{9_{46}}$ knot with a Lagrangian concordance $U\prec\Lambda$. The satellite $S(U,W)$ is the Legendrian right-handed trefoil $T$ with $tb=1$, and applying the satellite construction gives a Lagrangian concordance $C$ from $T$ to $S(\Lambda,W)$. Indecomposability conjecture. The Lagrangian concordance $C$ from $T$ to $S(\Lambda,W)$ is not decomposable. This would show that not all Lagrangian concordances are decomposable, contrary to the tempting conjecture mentioned immediately beforehand.