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In the Nice model of Solar System formation, Uranus and Neptune undergo an orbital upheaval, sweeping through a planetesimal disk. The region of the disk from which material is accreted by the ice giants during this phase of their evolution has not previously been identified. We perform direct N -body orbital simulations of the four giant planets to determine the amount and origin of solid accretion during this orbital upheaval. We find that the ice giants undergo an extreme bombardment event, with collision rates as high as ∼3 per hour assuming km-sized planetesimals, increasing the total planet mass by up to ∼0.35%. In all cases, the initially outermost ice giant experiences the largest total enhancement. We determine that, for some plausible planetesimal properties, the resulting atmospheric enrichment could potentially produce sufficient latent heat to alter the planetary cooling timescale according to existing models. Our findings suggest that substantial accretion during this phase of planetary evolution may have been sufficient to impact the atmospheric composition and thermal evolution of the ice giants, motivating future work on the fate of deposited solid material.