We derive dust masses (Mdust) from the spectral energy distributions of 58 post-starburst galaxies (PSBs). There is an anticorrelation between specific dust mass (Mdust/M ) and the time elapsed since the starburst ended, indicating that dust was either destroyed, expelled, or rendered undetectable over the ∼1 Gyr after the burst. The Mdust/M depletion timescale, , is consistent with that of the CO-traced , suggesting that dust and gas are altered via the same process. Extrapolating these trends leads to the Mdust/M and values of early-type galaxies (ETGs) within 1-2 Gyr, a timescale consistent with the evolution of other PSB properties into ETGs. Comparing Mdust and for PSBs yields a calibration, log , that allows us to place 33 PSBs on the Kennicutt-Schmidt (KS) plane, . Over the first ∼200-300 Myr, the PSBs evolve down and off of the KS relation, as their star formation rate (SFR) decreases more rapidly than . Afterwards, continues to decline whereas the SFR levels off. These trends suggest that the star formation efficiency bottoms out at 10−11 yr−1 and will rise to ETG levels within 0.5-1.1 Gyr 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 Mdust/M and 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.