A Feistel network splits a block into two halves L and R, then repeats a simple round: compute F(R, Ki), XOR the result into L, and swap. Because XOR is self-inverse and the swap is undone by another swap, the exact same circuit run with the round keys in reverse order decrypts — F itself never needs to be invertible. That's the trick that powers DES, Blowfish, TEA, and many others.
After a round: L' = R, R' = L ⊕ F(R, Ki). To invert, we want L and R back from L' and R'. Substitute R = L': L = R' ⊕ F(L', Ki). That's exactly the same round formula applied to (R', L') — swap the halves, apply the same F with the same key, swap again. So running the network with the round keys in reverse order undoes encryption. F can be anything — hash, S-box, table lookup — because it never has to be inverted; only XOR does the reversible heavy lifting.