  We have used a combination of neutron resonant spin-echo and triple-axis
spectroscopies to determine the energy and linewidth of the magnon resonance in
IPA-Cu(Cl$_{0.95}$Br$_{0.05}$)$_3$, a model spin-1/2 ladder antiferromagnet
where Br substitution induces bond randomness. We find that the bond defects
induce a blueshift, $\delta \Delta$, and broadening, $\delta \Gamma$, of the
magnon gap excitation compared to the pure compound. At temperatures exceeding
the energy scale of the inter-ladder exchange interactions, $\delta \Delta$ and
$\delta \Gamma$ are temperature independent within the experimental error, in
agreement with Matthiessen's rule according to which magnon-defect scattering
yields a temperature independent contribution to the magnon mean free path.
Upon cooling, $\delta \Delta$ and $\delta \Gamma$ become temperature dependent
and saturate at values lower than those observed at higher temperature,
consistent with the crossover from one-dimensional to two-dimensional spin
correlations with decreasing temperature previously observed in pure
IPA-CuCl$_3$. These results indicate limitations in the applicability of
Matthiessen's rule for magnon scattering in low-dimensional magnets.
