Presented in this thesis are the results of the BANFF near-detector fit as part of the T2K 2020 neutrino oscillation parameter constraint, with a focus on the implementation of four nucleon-removal energy parameters, $\Delta E_{\mathrm{rmv}}$. These parameters correspond to the systematic uncertainty associated with the energetic cost, $E_{\mathrm{rmv}}$, of liberating a bound nucleon from the ground state of a nucleus in quasielastic neutrino scattering. Previously the dominant source of systematic uncertainty on the extraction of the neutrino mass splitting term $\Delta m^2_{32}$(NO)/$|\Delta m^2_{31}|$(IO), an update of the nuclear model used for CCQE interactions at T2K from a relativistic Fermi gas model to a spectral function model and a new treatment of the systematic uncertainty on $E_{\mathrm{rmv}}$ has allowed the total bias on $\Delta m^2_{32}$ to be reduced by a factor of 2.8, and does not impact T2K's ability to exclude leptonic CP-conservation.
The fit to the ND280 data is an essential stage of the extraction of the PMNS mixing parameters from T2K's data in which the beam and interaction cross-section models common to ND280 and Super-Kamiokande are constrained by sampling the unoscillated beam. The ND280 data are shown to be consistent with the T2K model, reporting a p-value of $p=0.74$, an improvement on the previous ND280 fit $p=0.5$. A study of the postfit model shows an improved consistency with a p-value of $p=0.82$.
The impact of propagating biases in the fits to the ND280 data to the fits to Super-Kamiokande data on the constraints on $\Delta m^2_{32}$ and $\delta_{CP}$ are investigated, shown to be small, and covered by an additional uncertainty term in the likelihood driven by fits to alternative models. The overall contribution of the $E_{\mathrm{rmv}}$ systematic uncertainty to the total variance on $\Delta m^2_{32}$ using the 2020 (2018) T2K implementation was estimated to be $\sigma_{E_{\text{rmv}}}^2/\sigma_{\Delta m^2}^2=1(6)\%$.