The contribution of the K ⁺Λ channel to the Gerasimov-Drell-Hearn (GDH) sum rule has been calculated by using the models that fit the recent SAPHIR or CLAS differential cross-section data. It is shown that the two data sets yield quite different contributions. The contribution of this channel to the forward spin polarizability of the proton also has been calculated. It is shown too that the inclusion of the recent CLAS C _x and C _z data in the fitting data base does not significantly change the result of the present calculation. Results of the fit, however, reveal the role of the S ₁₁(1650), P ₁₁(1710), P ₁₃(1720), and P ₁₃(1900) resonances for the description of the C _x and C _z data. A brief discussion on the importance of these resonances is given. Measurements of the polarized total cross section σ _TT′ by the CLAS, LEPS, and MAMI collaborations are expected to verify this finding.