Fetal functional Magnetic Resonance Imaging (fMRI) has emerged as a powerful tool for investigating brain development in utero, holding promise for generating developmental disease biomarkers and supporting prenatal diagnosis. However, to date its clinical applications have been limited by unpredictable fetal and maternal motion during image acquisition. Even after spatial realigment, these cause spurious signal fluctuations confounding measures of functional connectivity and biasing statistical inference of relationships between connectivity and individual differences. As there is no ground truth for the brains functional structure, especially before birth, quantifying the quality of motion correction is challenging. In this paper, we propose evaluating the efficacy of different regression based methods for removing motion artifacts after realignment by assessing the residual relationship of functional connectivity with estimated motion, and with the distance between areas. Results demonstrate the sensitivity of our evaluations criteria to reveal the relative strengths and weaknesses among different artifact removal methods, and underscore the need for greater care when dealing with fetal motion.