  We compute the direct current resistivity of a scale-invariant,
$d$-dimensional strange metal with dynamic critical exponent $z$ and
hyperscaling-violating exponent $\theta$, weakly perturbed by a scalar operator
coupled to random-field disorder that locally breaks a $\mathbb{Z}_2$ symmetry.
Independent calculations via Einstein-Maxwell-Dilaton holography and memory
matrix methods lead to the same results. We show that random field disorder has
a strong effect on resistivity: charge carriers in the infrared are easily
depleted, as the relaxation time for momentum is surprisingly small. In the
course of our holographic calculation we use a non-trivial dilaton coupling to
the disordered scalar, allowing us to study a strongly-coupled scale invariant
theory with $\theta \ne 0$. Using holography, we are also able to determine the
disorder strength at which perturbation theory breaks down. Curiously, for
locally critical theories this breakdown occurs when the resistivity is
proportional to the entropy density, up to a possible logarithmic correction.
