Phase-contrast X-ray provides attenuation, phase-shift and small-angle-scatter in tissue in same scan yielding multi-contrast information about object, which has greatly benefitted breast-imaging, pre-clinical lung-imaging and bone imaging. A primary barrier for clinical adaptation of interferometric X-ray/CT for torso imaging is the manufacturing difficulty of large gratings. Large-gratings have to be stitched from smaller elements introducing errors such as gaps, errors in pitch, phase-jumps, tilts, causing imaging artifacts. Removing these artifacts will be an advancement towards clinical adaptability this multi-contrast modality. In this work we focus on the Talbot-Lau X-ray Interferometer and investigate effects of different grating defects in 1-D simulations. The grating spot defects include gaps, pitch errors, phase-height errors. We quantify the sum-squared error in reconstructed phase for different types of defects, showing most egregious artifacts for the pitch-errors. We developed two artifact correction methods in interference fringe patterns (i.e. before reconstruction) – an analytical and a neutral network approach. The analytical method (SWFT) uses Short- Window-Fourier-Transform to estimate the local phase-shift and attenuation due to the defect in the blank scans and then applies the correction for the with-objects scans. We also proposed a Regression Convolution Neural Network (R-CNN) to learn these errors and correct for them. Distinct sets of pitch artifacts were used each for training (300 datasets) and testing (300 datasets) with variety of levels of severity of artifacts for three different objects – sphere, ramp and slab. The algorithms performed well, reducing the artifacts from initial average normalized-mean-squared-error of 44.7% to 6.3% for SWFT and 7% for SWFT+R-CNN.