  A detection of excess cosmic microwave background (CMB) B-mode polarization
on large scales allows the possibility of measuring not only the amplitude of
these fluctuations but also their scale dependence, which can be parametrized
as the tensor tilt $n_T$. Measurements of this scale dependence will be
hindered by the secondary B-mode polarization anisotropy induced by
gravitational lensing. Fortunately, these contaminating B modes can be
estimated and removed with a sufficiently good estimate of the intervening
gravitational potential and a good map of CMB E-mode polarization. We present
forecasts for how well these gravitational lensing B modes can be removed,
assuming that the lensing potential can be estimated either internally from CMB
data or using maps of the cosmic infrared background (CIB) as a tracer. We find
that CIB maps are as effective as CMB maps for delensing at the noise levels of
the current generation of CMB experiments, while the CMB maps themselves will
ultimately be best for delensing at polarization noise below $\Delta_P$=1
$\mu$K-arcmin. At this sensitivity level, CMB delensing will be able to measure
$n_T$ to an accuracy of 0.02 or better, which corresponds to the tensor tilt
predicted by the consistency relation for single-field slow-roll models of
inflation with $r=0.2$. However, CIB-based delensing will not be sufficient for
constraining $n_T$ in simple inflationary models.
