  The current study aims to examine the impact of the boundary term on the
bending angle of light for a static spherically symmetric black hole in the
modified gravity described by the $f(\mathcal{T}, \mathcal{B})$ function. To
accomplish this objective, we employ the Ishihara \textit{et al.}~method, which
enables us to compute the deflection angle of light for a receiver and source
situated at finite distances from a lens object in a non-asymptotically flat
spacetime. This method considers the receiver's viewpoint, and the resulting
deflection angle diverges as the distance from the lens object increases, owing
to the non-asymptotically flat spacetime. Nevertheless, the divergence can be
regulated by the boundary term parameter $c_0$. For lower values of the
parameter $c_0$, the divergence can be minimized within the finite range of the
observer and source. Furthermore, we calculate the quasinormal modes of
massless scalar perturbations in the black hole's background using the
asymptotic iteration method (AIM) and Pad\'e averaged sixth-order
Wentzel-Kramers-Brillouin (WKB) approximation method. Our findings indicate
that the real quasinormal modes and damping rates are significantly impacted by
the model parameter $c_0$. Subsequently, we investigate two optical
characteristics of the black hole, namely the shadow and the emission rate. Our
results show that with an increase in the boundary term parameter $c_0$, the
shadow's size increases, and the evaporation rate decreases.
