SN1991bg-like supernovae are a distinct subclass of thermonuclear Type Ia supernovae (SNe Ia). Their spectral and photometric peculiarities indicate that their progenitors and explosion mechanisms differ from ‘normal’ SNe Ia. One method of determining information about supernova progenitors we cannot directly observe is to observe the stellar population adjacent to the apparent supernova explosion site to infer the distribution of stellar population ages and metallicities. We obtain integral field observations and analyse the spectra extracted from regions of projected radius $\sim\,\text{kpc}$ about the apparent SN explosion site for 11 91bg-like SNe in both early- and late-type galaxies. We utilise full-spectrum spectral fitting to determine the ages and metallicities of the stellar population within the aperture. We find that the majority of the stellar populations that hosted 91bg-like supernovae have little recent star formation. The ages of the stellar populations suggest that that 91bg-like SN progenitors explode after delay times of >6 Gyr, much longer than the typical delay time of normal SNe Ia, which peaks at $\sim$1 Gyr.