The electromagnetically induced transparency (EIT) effect realized by metasurfaces have potential for narrowband filtering due to their narrow bandwidth. In optics, bound states in the continuum (BIC) can produce strong localized resonances, which means that light can be trapped and stored for long periods of time to produce very high Q-factors. This has potential applications in designing highly efficient sensors and narrow bandpass filters. Here, we present two metal-flexible dielectric metasurfaces consisting of copper structures and polyimide substrates. Quasi BICs are obtained by breaking C2 symmetry of the metal structures. Resonance-captured quasi-BICs with ultra-high q-factor resonances satisfy the dark modes required to realize the EIT and couple to the bright modes in the structure to achieve narrowband filtering. The peak transmission rates are around 0.9 at 0.29 THz-0.32 THz and 0.23 THz-0.27 THz, respectively. Our results have practical implications for the realization of low-frequency terahertz communications.