  Intermediate-Luminosity Red Transients (ILRTs) are a class of observed
transient posited to arise from the production of an electron-capture supernova
from a super-asymptotic giant branch star within a dusty cocoon. In this paper,
we present a systematic analysis of narrow Na I D absorption as a means of
probing the circumstellar environment of these events. We find a wide diversity
of evolution in ILRTs in terms of line strength, time-scale, and shape. We
present a simple toy model designed to predict this evolution as arising from
ejecta from a central supernova passing through a circumstellar environment
wherein Na II is recombining to Na I over time. We find that while our toy
model can qualitatively explain the evolution of a number of ILRTs, the
majority of our sample undergoes evolution more complex than predicted. The
success of using the Na I D doublet as a diagnostic tool for studying
circumstellar material will rely on the availability of regular high-resolution
spectral observations of multiple ILRTs, and more detailed spectral modelling
will be required to produce models capable of explaining the diverse range of
behaviours exhibited by ILRTs. In addition, the strength of the Na I D
absorption feature has been used as a means of estimating the extinction of
sources, and we suggest that the variability visible in ILRTs would prevent
such methods from being used for this class of transient, and any others
showing evidence of variability
