Detectability maps obtained from injection recovery tests, showing upper limits on the abundances of the main near-infrared absorbers in the atmosphere of G 436 b. Specifically, we investigated H₂O (left panel), CH₄ (middle panel), and CO (right panel) across a range of metallicities and cloud deck altitudes. Dashed lines indicate the S/N = 5 contours (‘SN5’, S/N = 3 for CO denoted as ‘SN3’) obtained from CARMENES (white, five transits combined), CRIRES⁺ (red, one transit), and combining the results from both instruments (green). The dotted pink lines mark the S/N = 5 (S/N = 3 for CO) contours from Grasser et al. (2024), referred to as ‘G24’, using the same CRIRES⁺ dataset. For CO, an additional contour with a potential offset corrected is also shown as ‘G24 offset corrected’ (see discussion in Sect. 5.4). The dash-dotted brown line corresponds to the 99.7% upper limit from Fig. 3 in Knutson et al. (2014a), referred to as ‘K14’. The latter values were extracted from their respective figures. The dashed purple line represents the 68% upper limit placed by Mukherjee et al. (2025), referred to as ‘M25’. The area below each curve represents the discarded atmospheric parameter values.