  We predict surface-induced odd-frequency (odd-$\nu$) spin-triplet
superconducting pairing can be a veritable signature of Majorana bound states
(MBS) in a Josephson nodal $p$-wave superconductor ($p_{x}$)-spin flipper
(SF)-nodal $p$-wave superconductor ($p_{x}$) junction. Remarkably, in a
$p_{x}$-SF-$p_{x}$ Josephson junction three distinct phases emerge: the
topological phase featuring MBS, the topological phase without MBS, and the
trivial phase devoid of MBS. Surface odd-$\nu$ spin-triplet pairing is induced
only in the topological regime when MBS appears. In contrast, surface-induced
even-frequency (even-$\nu$) spin-triplet pairing is finite regardless of the
existence of MBS. Importantly, we find the surface induced odd-$\nu$
spin-triplet pairing is immune to disorder in the topological phase featuring
MBS, while in the trivial phase the surface induced even-$\nu$ spin-triplet
pairing is affected by disorder. Our study offers a potential means for
distinguishing the topological phase featuring MBS from both the trivial phase
as well as the topological phase devoid of MBS, primarily through the
observation of induced surface odd-$\nu$ spin-triplet superconductivity.
