  For a Legendrian $(2,n)$ torus knot or link with maximal Thurston-Bennequin
number, Ekholm, Honda, and K\'alm\'an constructed $C_n$ exact Lagrangian
fillings, where $C_n$ is the $n$-th Catalan number. We show that these exact
Lagrangian fillings are pairwise non-isotopic through exact Lagrangian isotopy.
To do that, we compute the augmentations induced by the exact Lagrangian
fillings $L$ to $\mathbb{Z}_2[H_1(L)]$ and distinguish the resulting
augmentations.
