  GCIRS 7, the brightest star in the Galactic central parsec, formed $6\pm2$
Myr ago together with dozens of massive stars in a disk orbiting the central
black-hole. It has been argued that GCIRS 7 is a pulsating body, on the basis
of photometric variability. We present the first medium-resolution ($R=500$),
K-band spectro-interferometric observations of GCIRS 7, using the GRAVITY
instrument with the four auxiliary telescopes of the ESO VLTI. We looked for
variations using two epochs, namely 2017 and 2019. We find GCIRS 7 to be
moderately resolved with a uniform-disk photospheric diameter of
$\theta^*_\text{UD}=1.55 \pm 0.03$ mas ($R^*_\text{UD}=1368 \pm 26$ $R_\odot$)
in the K-band continuum. The narrow-band uniform-disk diameter increases above
2.3 $\mu$m, with a clear correlation with the CO band heads in the spectrum.
This correlation is aptly modeled by a hot ($T_\text{L}=2368\pm37$ K),
geometrically thin molecular shell with a diameter of
$\theta_\text{L}=1.74\pm0.03$ mas, as measured in 2017. The shell diameter
increased ($\theta_\text{L}=1.89\pm0.03$ mas), while its temperature decreased
($T_\text{L}=2140\pm42$ K) in 2019. In contrast, the photospheric diameter
$\theta^*_\text{UD}$ and the extinction up to the photosphere of GCIRS 7
($A_{\mathrm{K}_\mathrm{S}}=3.18 \pm 0.16$) have the same value within
uncertainties at the two epochs. In the context of previous interferometric and
photo-spectrometric measurements, the GRAVITY data allow for an interpretation
in terms of photospheric pulsations. The photospheric diameter measured in 2017
and 2019 is significantly larger than previously reported using the PIONIER
instrument ($\theta_*=1.076 \pm 0.093$ mas in 2013 in the H band). The
parameters of the photosphere and molecular shell of GCIRS 7 are comparable to
those of other red supergiants that have previously been studied using
interferometry.
