We investigate the problem of restoring Mycenaean linear B clay tablets, dating from about 1400 B.C. to roughly 1200 B.C., by using text infilling methods based on machine learning models. Our goals here are: first to try to improve the results of the methods used in the related literature by focusing on the characteristics of the Mycenaean Linear B writing system (series D), second to examine the same problem for the first time on series A&B and finally to investigate transfer learning using series D as source and the smaller series A&B as target. Our results show promising results in the supervised learning tasks, while further investigation is needed to better exploit the merits of transfer learning.