We present the first detailed case study using quadratic estimators (QE) to diagnose and remove systematics present in observed Cosmic Microwave Background (CMB) maps. In this work we focus on the temperature to polarization leakage. We use an iterative QE analysis to remove systematics, in analogy to de-lensing, recovering the primordial B-mode signal and the systematic maps. We introduce a new Gaussian filtering scheme crucial to stable convergence of the iterative cleaning procedure and validate with comparisons to semi-analytical forecasts. We study the limitations of this method, by examining its performance on idealized simulations and we apply this method on realistic simulations generated for a LiteBIRD like experiment, where we assume varying de-lensing efficiencies. Finally, we quantify the systematic cleaning efficiency by presenting a likelihood analysis on the tensor to scalar ratio, r, and demonstrate that the blind cleaning results in an un-biased measurement of r, reducing the systematic induced B-mode power by nearly two orders of magnitude.