We investigate the single-photon scattering spectrum of a driven $\mathrm{\Lambda }$-type giant-atom system chirally coupled to a one-dimensional waveguide. By employing a real-space scattering approach, we obtain analytical solutions for the scattering amplitudes that remain valid in both Markovian and non-Markovian regimes. We observe that an external driving field induces a splitting of the transmission spectrum's dip into double dips, with the distance between the two dips increasing as the strength of the driving field increases. The chiral nature of the coupling allows for controlled switching between complete transmission and perfect reflection of incident photons. We find robust perfect transmission at specific phase values, independent of the driving field parameters. Moreover, in the non-Markovian regime, as the size of the giant atom increases, the oscillatory behavior of the scattering spectrum becomes more pronounced. Adjusting the giant-atom size enables control over the number of decoupling points as well as the number of complete reflection points.

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• Quantum information processing