  BaMn$_{2}$As$_{2}$ is an antiferromagnetic insulator where a metal-insulator
transition occurs with hole doping via the substitution of Ba with K. The
metal-insulator transition causes only a small suppression of the N\'eel
temperature ($T_\mathrm{N}$) and the ordered moment, suggesting that doped
holes interact weakly with the Mn spin system. Powder inelastic neutron
scattering measurements were performed on three different powder samples of
Ba$_{1-x}$K$_{x}$Mn$_{2}$As$_{2}$ with $x=$0, 0.125 and 0.25 to study the
effect of hole doping and metallization on the spin dynamics of these
compounds. We compare the neutron intensities to a linear spin wave theory
approximation to the $J_{1}-J_{2}-J_{c}$ Heisenberg model. Hole doping is found
to introduce only minor modifications to the exchange energies and spin gap.
The changes observed in the exchange constants are consistent with the small
drop of $T_\mathrm{N}$ with doping.
