It has been suggested that a class of chemically peculiar metal-poor stars called iron-rich metal-poor (IRMP) stars formed from molecular cores with metal contents dominated by thermonuclear supernova nucleosynthesis. If this interpretation is accurate, then IRMP stars should be more common in environments where thermonuclear supernovae were important contributors to chemical evolution. Conversely, IRMP stars should be less common in environments where thermonuclear supernovae were not important contributors to chemical evolution. At constant [Fe/H]<~-1, the Milky Way's satellite classical dwarf spheroidal (dSph) galaxies and the Magellanic Clouds have lower [{alpha}/Fe] than the Milky Way field and globular cluster populations. This difference is thought to demonstrate the importance of thermonuclear supernova nucleosynthesis for the chemical evolution of the Milky Way's satellite classical dSph galaxies and the Magellanic Clouds. We use data from the Sloan Digital Sky Survey Apache Point Observatory Galactic Evolution Experiment and Gaia to infer the occurrence of IRMP stars in the Milky Way's satellite classical dSph galaxies {eta}dSph and the Magellanic Clouds {eta}Mag, as well as in the Milky Way field {eta}MWF and globular cluster populations {eta}MWGC. In order of decreasing occurrence, we find {eta}dSph=0.07_-0.02_^+0.02^, {eta}_Mag_=0.037_-0.006_^+0.007^, {eta}_MWF_=0.0013_-0.0005_^+0.0006^, and a 1{sigma} upper limit {eta}MWGC<0.00057. These occurrences support the inference that IRMP stars formed in environments dominated by thermonuclear supernova nucleosynthesis and that the time lag between the formation of the first and second stellar generations in globular clusters was longer than the thermonuclear supernova delay time.