  We investigate the local preservation of Birkhoff-James orthogonality at a
point by a linear operator on a finite-dimensional Banach space and illustrate
its importance in understanding the action of the operator in terms of the
geometry of the concerned spaces. In particular, it is shown that such a study
is related to the preservation of k-smoothness and the extremal properties of
the unit ball of a Banach space. As an application of the results obtained in
this direction, we obtain a refinement of the well-known
Blanco-Koldobsky-Turnsek characterization of isometries on some polyhedral
Banach spaces, including $ \ell_{\infty}^n, \ell_1^n. $
