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Abstract Gravitational lenses can magnify distant galaxies, allowing us to discover and characterize the stellar populations of intrinsically faint, quiescent galaxies that are otherwise extremely difficult to directly observe at high redshift from ground-based telescopes. Here, we present the spectral analysis of two lensed, quiescent galaxies atz≳ 1 discovered by theASTRO 3D Galaxy Evolution with Lensessurvey:AGEL1323 (M_*∼ 10^11.1M_⊙,z= 1.016,μ∼ 14.6) andAGEL0014 (M_*∼ 10^11.5M_⊙,z= 1.374,μ∼ 4.3). We measured the age, [Fe/H], and [Mg/Fe] of the two lensed galaxies using deep, rest-frame-optical spectra (S/N ≳40 Å⁻¹) obtained on the Keck I telescope. The ages ofAGEL1323 andAGEL0014 are ${5.6}_{-0.8}^{+0.8}$Gyr and ${3.1}_{-0.3}^{+0.8}$Gyr, respectively, indicating that most of the stars in the galaxies were formed less than 2 Gyr after the Big Bang. Compared to nearby quiescent galaxies of similar masses, the lensed galaxies have lower [Fe/H] and [Mg/H]. Surprisingly, the two galaxies have comparable [Mg/Fe] to similar-mass galaxies at lower redshifts, despite their old ages. Using a simple analytic chemical evolution model connecting the instantaneously recycled element Mg with the mass-loading factors of outflows averaged over the entire star formation history, we found that the lensed galaxies may have experienced enhanced outflows during their star formation compared to lower-redshift galaxies, which may explain why they quenched early.