The physical process whereby a carbon-oxygen white dwarf explodes as a Type Ia supernova (SN Ia) remains highly uncertain. The degree of neutronization in SN Ia ejecta holds clues to this process because it depends on the mass and the metallicity of the stellar progenitor, and on the thermodynamic history prior to the explosion. We report on a new method to determine ejecta neutronization using Ca and S lines in the X-ray spectra of Type Ia supernova remnants (SNRs). Applying this method to \textit{Suzaku} data of Tycho, Kepler, 3C 397, G337.2$-$0.7 in the MW, and N103B in the LMC, we find that the neutronization of the ejecta in N103B is comparable to that of Tycho and Kepler, which suggests that progenitor metallicity is not the only source of neutronization in SNe Ia. We then use a grid of SN Ia explosion models to infer the metallicities of the stellar progenitors of our SNRs. The implied metallicities of 3C 397, G337.2$-$0.7, and N103B are major outliers compared to the local stellar metallicity distribution functions, indicating that progenitor metallicity can be ruled out as the origin of neutronization for these SNRs. Although the relationship between ejecta neutronization and equivalent progenitor metallicity is subject to uncertainties stemming from the $^{12}$C$\,$+$^{16}$O reaction rate, which affects the Ca/S mass ratio, our main results are not sensitive to these details. ; Comment: 11 pages, 6 figures, submitted to the ApJ