  We study the gravitational edge mode in the $\mathcal{N}=1$
Jackiw-Teitelboim~(JT) supergravity on the disk and it $osp(2|1)$ BF
formulation. We revisit the derivation of the finite-temperature Schwarzian
action in the conformal gauge of the bosonic JT gravity through wiggling
boundary and the frame fluctuation descriptions. Extending our method to
$\mathcal{N}=1$ JT supergravity, we derive the finite-temperature
super-Schwarzian action for the edge mode from both the wiggling boundary and
the superframe field fluctuation. We emphasize the crucial role of the
supersymmetric version of the inversion formula in elucidating the relation
between the isometry and the $OSp(2|1)$ gauging of the super-Schwarzian action.
In $osp(2|1)$ BF formulation, we discuss the asymptotic AdS condition. We
employ the Iwasawa-like decomposition of $OSp(2|1)$ group element to derive the
super-Schwarzian action at finite temperature. We demonstrate that the
$OSp(2|1)$ gauging arises from inherent redundancy in the Iwasawa-like
decomposition. We also discuss the path integral measure obtained from the Haar
measure of $OSp(2|1)$.
