  We consider the Larkin model of a directed polymer with Gaussian-distributed
random forces, with the addition of a resetting process whereby the transverse
position of the end-point of the polymer is reset to zero with constant rate
$r$. We express the average over disorder of the mean time to absorption by an
absorbing target at a fixed value of the transverse position. Thanks to the
independence properties of the distribution of the random forces, this
expression is analogous to the mean time to absorption for a diffusive particle
under resetting, which possesses a single minimum at an optimal value $r^\ast$
of the resetting rate . Moreover, the mean time to absorption can be expanded
as a power series of the amplitude of the disorder, around the value $r^\ast$
of the resetting rate. We obtain the susceptibility of the optimal resetting
rate to disorder in closed form, and find it to be positive.
