Airborne ultrasound tactile display (AUTD) is used to provide non-contact tactile sensations with specific foci sound fields through the optimization of transducer phases. However, most existing optimization approaches are not directly applicable in case of an inhomogeneous medium, such as in the presence of obstacles between the AUTD and objective sound field. Certain methods can perform optimizations by considering the sound-scattering surfaces of the obstacles to compute the transmission matrix, which requires several complex measurements. This study proposed two methods to reconstruct the sound field under an inhomogeneous medium, wherein the need to calculate the impact of the obstacles was eliminated. The two methods are Bayesian optimization and greedy algorithm with brute-force search. Further, the process of the foci field generation was assumed as a black box. The proposed methods require only the pressure intensity at the control point generated by the input phases, discarding the need for transmission matrix in the presence of obstacles. Moreover, these methods offer the advantage of optimization of the phases in the presence of obstacles. This study explains the working of proposed methods in different forms of foci fields encountering obstacles.