  Many models of the early universe predict that there should be primordial
tensor perturbations. These leave an imprint into the temperature and
polarisation anisotropies of the cosmic microwave background (CMB). The
differential equation describing the primordial tensor perturbations is a
second order differential equation and thus has two solutions. Canonically, the
decaying solution of this equation in radiation domination is dropped as it
diverges at early times and on superhorizon scales while it is then suppressed
at late times. Furthermore, if there is an inflationary phase prior to the
radiation domination phase, the amplitude of the decaying mode will also be
highly suppressed as it enters the radiation phase, thus its effect will be
negligible. In this study we remain agnostic to the early universe models
describing pre-radiation domination physics and allow this mode to be present
and see what effect it has on the CMB anisotropies. We find that the decaying
mode, if normalised at the same time on subhorizon scales as the growing mode
leaves an imprint on the CMB anisotropies that is identical to the growing
mode. Contrary to expectation, on large scales both modes are poorly
constrained for a scale invariant spectrum, and the apparent divergence of the
decaying mode does not lead to a divergent physical observable. Quantitatively,
the decaying mode can be more constrained both from temperature and
polarisation anisotropies. We use a model independent, non-parametric, approach
to constrain both of these primordial tensor perturbations using the
temperature and polarisation anisotropies. We find that both modes are best
constrained at the reionisation and recombination bumps and crucially, at the
reionisation bump the decaying mode can be distinguished from the growing mode.
