We use numerical mass density profiles from the TNG50 simulation to study the impact of gravitational milli-lensing by dark matter subhaloes on the images of lensed quasars. Specifically, we study the formation of subimages and the probability of their detection. For high-concentration density profiles, the mass determines the amplitude of the image splitting, but for less compact subhaloes, the separation between subimages also depends on the interplay between the inner slope of the density profile and the macro-magnification induced by the lens galaxy. For a log-slope m = ‑2, close to the mean value of TNG50 density profiles, the detection possibilities increase with respect to less steep, commonly used, analytical models. For typical values of the concentration, 104 ≤ Cv ≤ 106, and macro-magnification μ ≥ 10, subhaloes in the entire studied mass range (Msh ≥ 3.5 × 108M⊙) can produce separations between subimages detectable with the Hubble Space Telescope or JWST. Considering the absence of reported image splitting in optical observations of lensed quasars, we establish an upper limit on the subhaloes mass fraction , consistent within uncertainties with the abundance of lensing-efficient subhaloes directly inferred from the TNG50 simulation, . We show that subhalo density profiles that were initially proposed to explain anomalies in the gravitational arcs of three lensed quasar systems, have also the potential to cause observable point image splitting. This presents an intriguing statistical puzzle when comparing the absence of image splitting in 400 quasar images to the three claimed detections of subhaloes in a small sample of modeled gravitational arcs.