The optical properties of KCa2Fe4As4F2 (K12442, Tc = 33.5 K) and KCa2(Fe0.95Ni0.05)4As4F2 (Ni-K12442, Tc = 29 K) have been examined at a large number of temperatures. For both samples, a nodeless superconducting gap is clearly observed in the optical conductivity at 5 K. The superconducting gap ∆ ≃ 8.7 meV (2∆/kBTc ≃ 6.03) in K12442, pointing towards strong-coupling Cooper pairs, but in sharp contrast, ∆ ≃ 4.6 meV (2∆/kBTc ≃ 3.68) in Ni-K12442, which agrees with the BCS weak-coupling pairing state. More intriguingly, below T * ≃ 75 K, the optical conductivity of K12442 reveals a pseudogap that smoothly evolves into the superconducting gap below Tc, while no such behavior is detected in the electron-doped Ni-K12442. The comparison between the two samples hints that the pseudogap and strong-coupling Cooper pairs in K12442 may be intimately related to the shallow and incipient bands.