We present constraints on the dust continuum flux and inferred gas content of a gravitationally lensed massive quiescent galaxy at z = 1.883 +/- 0.001 using AzTEC 1.1 mm imaging with the Large Millimeter Telescope. MRGS0851 appears to be a prototypical massive compact quiescent galaxy, but evidence suggests that it experienced a centrally concentrated rejuvenation event in the last 100 Myr. This galaxy is undetected in the AzTEC image but we calculate an upper limit on the millimeter flux and use this to estimate the H-2 mass limit via an empirically calibrated relation that assumes a constant molecular-gas-to-dust ratio of 150. We constrain the 3s upper limit of the H-2 fraction from the dust continuum in MRG-S0851 to be M-H2/M-star