  It is commonly assumed that the stochastic background of gravitational waves
on cosmological scales follows an almost scale-independent power spectrum, as
generically predicted by the inflationary paradigm. However, it is not
inconceivable that the spectrum could have strongly scale-dependent features,
generated, e.g., via transient dynamics of spectator axion-gauge fields during
inflation. Using the temperature and polarisation maps from the \textit{Planck}
and BICEP/Keck datasets, we search for such features, taking the example of a
log-normal bump in the primordial tensor spectrum at CMB scales. We do not find
any evidence for the existence of bump-like tensor features at present, but
demonstrate that future CMB experiments such as LiteBIRD and CMB-S4 will
greatly improve our prospects of determining the amplitude, location and width
of such a bump. We also highlight the role of delensing in constraining these
features at angular scales $\ell\gtrsim 100$.
