The spin-to-charge conversion in Permalloy (Py)/Cu/Bi₂Se₃ is tunable by changing the Cu layer thickness. The conversion rate was studied using the spin pumping technique. The inverse Edelstein effect (IEE) length λ_IEE is found to increase up to ~2.7 nm when a 7 nm Cu layer is introduced. Interestingly, the maximized λ_IEE is obtained when the effective spin-mixing conductance (and thus J_s) is decreased due to Cu insertion. The monotonic increase in λ_IEE with decreasing J_s suggests that the IEE relaxation time (τ) is enhanced due to the additional tunnelling barrier (Cu layer) that limits the interfacial transmission rate. The results demonstrate the importance of interface engineering in the magnetic heterostructure of Py/topological insulators (TIs), the key factor in optimizing spin-to-charge conversion efficiency.