We explore the relationship between the models for progenitor systems of Type Ia supernovae and the properties of the supernova remnants that evolve after the explosion. Most models for Type Ia progenitors in the single-degenerate scenario predict substantial outflows during the presupernova evolution. Expanding on previous work, we estimate the imprint of these outflows on the structure of the circumstellar medium at the time of the supernova explosion, and the effect that this modified circumstellar medium has on the evolution of the ensuing supernova remnant. We compare our simulations with the observational properties of known Type Ia supernova remnants in the Galaxy (Kepler, Tycho, SN 1006), the Large Magellanic Cloud (0509-67.5, 0519-69.0, N103B), and M31 (SN 1885). We find that optically thick outflows from the white dwarf surface (sometimes known as "accretion winds") with velocities above 200 km s-1 excavate large low-density cavities around the progenitors. Such large cavities are incompatible with the dynamics of the forward shock and the X-ray emission from the shocked ejecta in all the Type Ia remnants that we have examined.

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