The Taiji space gravitational wave detection mission employs laser interferometry to measure picometer-level distance variations induced by gravitational waves. Attitude jitter in both satellites and movable optical subassemblies (MOSA) generates tilt-to-length (TTL) coupling noise that critically degrades detection sensitivity. Therefore, it is necessary to fit and subtract TTL noise during the data processing stage. To address this challenge, we propose an iterative TTL noise suppression algorithm for post-processing. First, a first-order linear approximation model of TTL noise is established and incorporated into the time-delay interferometry (TDI) combinations to derive its expression in TDI outputs. We subsequently perform initial maximum likelihood estimation of the TTL coupling coefficients, subtract the preliminary TTL noise estimate from the TDI data to characterize the residual baseline noise statistics, and reincorporate these statistics into the updated likelihood function for subsequent TTL coefficient estimation. Through ten iterative cycles, we achieve a refined baseline noise model. Finally, The posterior distribution of the TTL coefficients is obtained via the Markov Chain Monte Carlo (MCMC) method, thereby accomplishing the precise fitting of the TTL noise and consequently achieving effective noise suppression. Results demonstrate that over 80% of estimated coefficients fall within three standard deviations, and more than 80% of the coefficient estimates deviate from the true values by less than 0.1 mm/rad. For various levels of TTL coefficients, the residual TTL noise after suppression is one order of magnitude lower than the secondary noise, demonstrating a certain degree of robustness. This is particularly applicable to real detection scenarios where the noise floor model is unknown, meeting the requirements for space-based gravitational wave detection.