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Layered heterostructures of TaS₂, such as the bilayer 1T/1H-TaS₂ and bulk 4H_b-TaS₂ have recently been in the spotlight due to Mott physics, the putative Kondo effect and topological superconductivity. There, the filling of the flat band originating from the 1T charge density wave (Star of David) plays a vital role. However, the position of the flat band and its occupation are controversial between different reports. In this work, we examined the electronic structures of the bilayer 1T/1H-TaS₂ and focused on the charge transfer between 1T and 1H layers. We found that the charge transfer is sensitive to the 1T/1H interlayer distance. Consequently, the flat band is empty in the equilibrium distance but turns to partially occupied when increasing the layer separation. Furthermore, we found that graphite substrate may also increase the flat band filling. Our work rationalizes that discrepancies in experiments may originate from the varied interlayer distance and/or underlying substrate and paves a practical pathway to tune the Mott physics.