We will present rigorous analysis for the direct scattering theory of perturbed Kadomtsev-Petviashvili II (KPII) one line solitons, the simplest case in Boiti-Pempinelli-Pogrebkov's inverse scattering theories of the KPII equation. Namely, for generic small perturbation of the one line soliton, the existence of the eigenfunction is proved by establishing uniform estimates of the Green function and the Cauchy integral equation for the eigenfunction is justified by non-uniform estimates of the spectral transformation.