Both Pluto and Triton possess thin, N_2_-dominated atmospheres controlled by sublimation of surface ices. We aim to constrain the influx and ablation of interplanetary dust grains into the atmospheres of both Pluto and Triton in order to estimate the rate at which oxygen-bearing species are introduced into both atmospheres. We use (i) an interplanetary dust dynamics model to calculate the flux and velocity distributions of interplanetary dust grains relevant for both Pluto and Triton and (ii) a model for the ablation of interplanetary dust grains in the atmospheres of both Pluto and Triton. We sum the individual ablation profiles over the incoming mass and velocity distributions of interplanetary dust grains in order to determine the vertical structure and net deposition of water to both atmospheres. Our results show that <2% of silicate grains ablate at either Pluto or Triton while approximately 75% and >99% of water ice grains ablate at Pluto and Triton, respectively. From ice grains, we calculate net water influxes to Pluto and Triton of ~3.8kg/d (8.5x10^3^H_2_O/cm^2^/s) and ~370kg/d (6.2x10^5^H_2_O/cm^2^/s), respectively. The significant difference in total water deposition between Pluto and Triton is due to the presence of Triton within Neptune's gravity well, which both enhances interplanetary dust particle (IDP) fluxes due to gravitational focusing and accelerates grains before entry into Triton's atmosphere, thereby causing more efficient ablation. We conclude that water deposition from dust ablation plays only a minor role at Pluto due to its relatively low flux. At Triton, water deposition from IDPs is more significant and may play a role in the alteration of atmospheric and ionospheric chemistry. We also suggest that meteoric smoke and smaller, unablated grains may serve as condensation nuclei for the formation of hazes at both worlds.