The ability to tune the twist angle between different layers of two-dimensional (2D) materials has enabled the creation of electronic flat bands artificially, leading to exotic quantum phases. When a twisted blilayer of graphene (tBLG) is placed at the van der Waals proximity to a semiconducting layer of transition metal dichalcogenide (TMDC), such as WSe2, the emergent phases in the tBLG can fundamentally modify the functionality of such heterostructures. Here we have performed photoresponse measurements in few-layer-WSe2/tBLG heterostructure, where the mis-orientation angle of the tBLG layer was chosen to lie close to the magic angle of 1.1°. Our experiments show that the photoresponse is extremely sensitive to the band structure of tBLG and gets strongly suppressed when the Fermi energy was placed within the low-energy moiré bands. Photoresponse could however be recovered when Fermi energy exceeded the moiré band edge where it was dominated by the photogating effect due to transfer of charge between the tBLG and the WSe2 layers. Our observations suggest the possibility of the screening effects from moiré flat bands that strongly affect the charge transfer process at the WSe2/tBLG interface, which is further supported by time-resolved photo-resistance measurements.