Context. The precise determination of the present-day expansion rate of the Universe, expressed through the Hubble constant H₀, is one of the most pressing challenges in modern cosmology. Assuming flat ΛCDM, H₀ inference at high redshift using cosmic microwave background data from Planck disagrees at the 4.4σ level with measurements based on the local distance ladder made up of parallaxes, Cepheids, and Type Ia supernovae (SNe Ia), often referred to as Hubble tension. Independent cosmological-model-insensitive ways to infer H₀ are of critical importance. Aims. We apply an inverse distance ladder approach, combining strong-lensing time-delay distance measurements with SN Ia data. By themselves, SNe Ia are merely good indicators of relative distance, but by anchoring them to strong gravitational lenses we can obtain an H₀ measurement that is relatively insensitive to other cosmological parameters. Methods. A cosmological parameter estimate was performed for different cosmological background models, both for strong-lensing data alone and for the combined lensing + SNe Ia data sets. Results. The cosmological-model dependence of strong-lensing H₀ measurements is significantly mitigated through the inverse distance ladder. In combination with SN Ia data, the inferred H₀ consistently lies around 73–74 km s⁻¹ Mpc⁻¹, regardless of the assumed cosmological background model. Our results agree closely with those from the local distance ladder, but there is a > 2σ tension with Planck results, and a ∼1.5σ discrepancy with results from an inverse distance ladder including Planck, baryon acoustic oscillations, and SNe Ia. Future strong-lensing distance measurements will reduce the uncertainties in H₀ from our inverse distance ladder.