  Blind cleaning methods are currently the preferred strategy for handling
foreground contamination in single-dish HI intensity mapping surveys. Despite
the increasing sophistication of blind techniques, some signal loss will be
inevitable across all scales. Constructing a corrective transfer function using
mock signal injection into the contaminated data has been a practice relied on
for HI intensity mapping experiments. However, assessing whether this approach
is viable for future intensity mapping surveys where precision cosmology is the
aim, remains unexplored. In this work, using simulations, we validate for the
first time the use of a foreground transfer function to reconstruct power
spectra of foreground-cleaned low-redshift intensity maps and look to expose
any limitations. We reveal that even when aggressive foreground cleaning is
required, which causes ${>}\,50\%$ negative bias on the largest scales, the
power spectrum can be reconstructed using a transfer function to within
sub-percent accuracy. We specifically outline the recipe for constructing an
unbiased transfer function, highlighting the pitfalls if one deviates from this
recipe, and also correctly identify how a transfer function should be applied
in an auto-correlation power spectrum. We validate a method that utilises the
transfer function variance for error estimation in foreground-cleaned power
spectra. Finally, we demonstrate how incorrect fiducial parameter assumptions
(up to ${\pm}100\%$ bias) in the generation of mocks, used in the construction
of the transfer function, do not significantly bias signal reconstruction or
parameter inference (inducing ${<}\,5\%$ bias in recovered values).
