Comparison of the derived transmission spectrum of V1298 Tau c for a fixed and free limb darkening fit to the light curves (upper panel) and corresponding 1σ uncertainties for each each spectroscopic bin (lower panel). We fix the limb darkening to i) linear limb darkening coefficients derived from the primary transit of V1298 Tau b (Barat et al. 2024) shown in red ii) model limb darkening coefficients derived from EXOCTK (Sect. 4.2 and Fig. F.2) shown in orange. The transmission spectrum derived using free linear limb darkening coefficients for planet c is shown in blue. The median subtracted transmission spectra in all three cases are consistent within 1σ of each other for all channels. A comparison between the transit depth uncertainty for the free and fixed limb darkening cases shows that fixing the limb darkening reduces the transit depth uncertainty by 5-10% for each channel.