Top: from left to right: the real-space two-point correlation function, the projected correlation function, the monopole, and the quadrupole of the correlation function for samples with number densities of 0.0316 (black lines), 0.01 (red lines), and 0.00316 h³ Mpc⁻³ (blue lines). Solid lines represent the standard MTNG-DMO samples, while dashed lines correspond to the clustering from the modified MTNG-DMO simulation, where satellite positions and velocities were adjusted to mimic those of the hydrodynamic MTNG run (MTNG-DMO_mod). Bottom: ratio of the clustering between MTNG-DMO_mod and MTNG-DMO for the two-point, projected, and monopole correlation functions. For the quadrupole (rightmost panel), we show the difference rather than the ratio to avoid discontinuities when the signal crosses zero.