  We address a current caveat in the deconvolution of the Primordial Power
Spectrum (PPS), from observed Cosmic Microwave Background (CMB) temperature
anisotropy, in the presence of weak lensing of the CMB by the large scale
structure (LSS) in the Universe. Richardson-Lucy (RL) deconvolution algorithm
has been used in the context of reconstructing a free-form PPS, $P_R(k)$ from
the observed lensed CMB temperature anisotropy power spectrum
$\widetilde{C}_{\ell}^{TT}$. We propose and demonstrate that the RL algorithm
works in the context of a non-linear convolution where the non-linear
contribution is small, such as the effect of weak lensing of the
$\widetilde{C}_{\ell}^{TT}$, for the deconvolution of the PPS from it. The
Non-Linear Iterative Richardson-Lucy (NIRL) algorithm is successful at both
convergence, as well as fidelity, in reconstructing features in some underlying
PPS. This makes PPS reconstruction efforts more robust in accounting for the
weak lensing effect in the CMB temperature observations. No prior assumptions
on the PPS are involved during the iterative delensing process, and distinct
improvement is noted over a power-law template based delensing approach used
earlier, at the cost of moderately increased computational cost due to the NIRL
reconstruction kernel.
