In this paper, we present the estimation of systematics related to the halo occupation distribution (HOD) modeling in the baryon acoustic oscillations (BAO) distance measurement of the Dark Energy Spectroscopic Instrument (DESI) 2024 analysis. This paper focuses on the study of HOD systematics for luminous red galaxies (LRG). We consider three different HOD models for LRGs, including the base 5-parameter vanilla model and two extensions to it, that we refer to as baseline and extended models. The baseline model is described by the 5 vanilla HOD parameters, an incompleteness factor and a velocity bias parameter, whereas the extended one also includes a galaxy assembly bias and a satellite profile parameter. We utilize the 25 dark matter simulations available in the AbacusSummit simulation suite at z = 0.8 and generate mock catalogs for our different HOD models. To test the impact of the HOD modeling in the position of the BAO peak, we run BAO fits for all these sets of simulations and compare the best-fit BAO-scaling parameters alpha(iso) and alpha(AP) between every pair of HOD models. We do this for both Fourier and configuration spaces independently, using post-reconstruction measurements. We find a 3.3 sigma detection of HOD systematic for alpha(AP) in configuration space with an amplitude of 0.19%. For the other cases, we did not find a 3 sigma detection, and we decided to compute a conservative estimation of the systematic using the ensemble of shifts between all pairs of HOD models. By doing this, we quote a systematic with an amplitude of 0.07% in alpha(iso) for both Fourier and configuration spaces; and of 0.09% in alpha(AP) for Fourier space.