We derive dust masses (M_dust_) from the spectral energy distributions of 58 post-starburst galaxies (PSBs). There is an anticorrelation between specific dust mass (M_dust_/M_*_) and the time elapsed since the starburst ended, indicating that dust was either destroyed, expelled, or rendered undetectable over the ~1Gyr after the burst. The M_dust_/M_*_ depletion timescale, 205_-37_^+58^Myr, is consistent with that of the CO-traced M_H2_/M_*_, suggesting that dust and gas are altered via the same process. Extrapolating these trends leads to the M_dust_/M_*_ and M_H2_/M_*_ values of early-type galaxies (ETGs) within 1-2Gyr, a timescale consistent with the evolution of other PSB properties into ETGs. Comparing Mdust and M_H2_ for PSBs yields a calibration, log M_H2_=0.45logM_dust_+6.02, that allows us to place 33 PSBs on the Kennicutt-Schmidt (KS) plane, {Sigma}SFR-{Sigma}M_H2_. Over the first ~200-300Myr, the PSBs evolve down and off of the KS relation, as their star formation rate (SFR) decreases more rapidly than M_H2_. Afterwards, M_H2_ continues to decline whereas the SFR levels off. These trends suggest that the star formation efficiency bottoms out at 10^-11^/yr and will rise to ETG levels within 0.5-1.1Gyr afterwards. The SFR decline after the burst is likely due to the absence of gas denser than the CO-traced H2. The mechanism of the M_dust_/M_*_ and M_H2_/M_*_ decline, whose timescale suggests active galactic nucleus/low-ionization nuclear emission-line region feedback, may also be preventing the large CO-traced molecular gas reservoirs from collapsing and forming denser star-forming clouds.