  We examine the contribution of tensor modes, in addition to the dominant
scalar ones, on the temperature anisotropies of the cosmic microwave background
(CMB). To this end, we analyze in detail the temperature two-point angular
correlation function $C(\theta)$ from the Planck 2018 dataset, focusing on
large angles ($\theta \gtrsim 120^{\circ}$) corresponding to small $\ell$
multipoles. A hierarchical set of infrared cutoffs are naturally introduced to
the scalar and tensor power spectra of the CMB by invoking an extra
Kaluza-Klein dimension compactifying at about the GUT scale between the Planck
epoch and the start of inflation. We associate this set of lower scalar and
tensor cutoffs with the parity of the multipole expansion of the $C(\theta)$
function. By fitting the Planck 2018 data we compute the multipole coefficients
thereby reproducing the well-known odd-parity preference in angular
correlations seen by all three satellite missions COBE, WMAP and Planck. Our
fits improve significantly once tensor modes are included in the analysis,
hence providing a hint of the imprints of primordial gravitational waves on the
temperature correlations observed in the CMB today. To conclude we suggest a
relationship between, on the one hand, the lack of (positive) large-angle
correlations and the odd-parity dominance in the CMB and, on the other hand,
the effect of primordial gravitational waves on the CMB temperature
anisotropies.
