BAO and CMB data are somewhat discrepant when interpreted in the context of ΛCDM, discrepancies that show up as a matter density deficit and as a CMB lensing excess. One possible resolution is an increased optical depth to scattering off of free electrons in the post-recombination universe, τ, a possibility raised by Sailer et al. 2025 and Jhaveri et al. 2025. Since Planck measurements of the low-ℓ polarization reionization bump already constrain τ from standard stellar-driven reionization at z < 10, we investigate additional optical depth sourced by transient or partial reionization at higher redshift from exotic processes. For specificity, we explore the impact of Hawking radiation from a monochromatic spectrum of primordial black holes, retaining the high-ℓ TT/TE/EE data that constrain such histories and varying the reionization redshift jointly. We find that the CMB data do not significantly prefer these additional signals: the boost is prior-sensitive and at most ∆τ ≃ 0.008, well short of the ∆τ ≃ 0.03 that would completely eliminate the moderate discrepancy. The matter density deficit and the lensing excess are not significantly eased: we explain why, tracing it to compensation from the reionization redshift and the residual PBH signal at ℓ> 30.