T2*-weighted gradient echo MR imaging is strongly impacted by subject head motion due to motion-related changes in B0 inhomogeneities. Within the oxygenation-sensitive mqBOLD protocol, even mild motion during the acquisition of the T2*-weighted data propagates into errors in derived quantitative parameter maps. In order to correct these images without the need of repeated measurements, we propose to learn a classification of motion-affected k-space lines. To test this, we perform realistic motion simulations including motion-induced field inhomogeneity changes for supervised training. To detect the presence of motion in each phase encoding line, we train a convolutional neural network, leveraging the multi-echo information of the T2*-weighted images. The proposed network accurately detects motion-affected k-space lines for simulated displacements of $\geq$ 0.5mm (accuracy on test set: 92.5%). Finally, we show example reconstructions where we include these classification labels as weights in the data consistency term of an iterative reconstruction procedure, opening up exciting opportunities of k-space line detection in combination with more powerful reconstruction methods.