  The MRS is one of the four observing modes of JWST/MIRI. Using JWST in-flight
data of unresolved (point) sources, we can derive the MRS absolute spectral
response function (ASRF) starting from raw data. Spectral fringing plays a
critical role in the derivation and interpretation of the MRS ASRF. In this
paper, we present an alternative way to calibrate the data. Firstly, we aim to
derive a fringe correction that accounts for the dependence of the fringe
properties on the MIRI pupil illumination and detector pixel sampling of the
point spread function. Secondly, we aim to derive the MRS ASRF using an
absolute flux calibrator observed across the full 5 to 28 $\mu$m wavelength
range of the MRS. Thirdly, we aim to apply the new ASRF to the spectrum of a G
dwarf and compare with the output of the JWST/MIRI default data reduction
pipeline. Finally, we examine the impact of the different fringe corrections on
the detectability of molecular features in the G dwarf and K giant. The
absolute flux calibrator HD 163466 (A-star) is used to derive tailored point
source fringe flats at each of the default dither locations of the MRS. The
fringe-corrected point source integrated spectrum of HD 163466 is used to
derive the MRS ASRF using a theoretical model for the stellar continuum. A
cross-correlation is run to quantify the uncertainty on the detection of CO,
SiO, and OH in the K giant and CO in the G dwarf for different fringe
corrections. The point-source-tailored fringe correction and ASRF are found to
perform at the same level as the current corrections, beating down the fringe
contrast to the sub-percent level, whilst mitigating the alteration of real
molecular features. The same tailored solutions can be applied to other MRS
unresolved targets. A pointing repeatability issue in the MRS limits the
effectiveness of the tailored fringe flats is at short wavelengths.
