Comparison of the inferred D_d, D_s/D_ds, D_Δt, and λ_int in different cases. Case 1 (orange): The distance measurements directly from single time-delay mock lens without assuming any cosmological model. Case 2 (blue): The distance measurements under the assumption of the flat wCDM model with Ω_m = [0.05, 1.0], Ω_de = 1 − Ω_m, w = [ − 2.5, 0.5], and H₀ uniform in [0,150] km s⁻¹ Mpc⁻¹. Case 3 (black): The distance measurements under the assumption of the ΛCDM model with Ω_m = [0.05, 1.0], Ω_Λ = 1 − Ω_m, and H₀ uniform in [0,150] km s⁻¹ Mpc⁻¹ Case 4: (green): The distance measurements from single time-delay mock lens, Pantheon dataset, and BAO dataset by using splines with free Ω_k. Case 5 (red): The distance measurements from single time-delay mock lens, Pantheon dataset, and BAO dataset by using splines with Ω_k = 0. For the cases (green and red) that do not assume a particular cosmological model, the constraining power on λ_int is comparable to the cases (blue and black) with an assumption of having a underlying cosmological model.