Dataset for Modulated Kondo screening along magnetic mirror twin boundaries in monolayer MoS2. STM and STS were carried out at a base operating temperature of T0 = 0.35K after in-situ transfer from the preparation chamber. STS was performed with the lock-in technique, at modulation frequency 907.0Hz. STM images are taken in constant current mode. Some of the data in Fig. 3d was taken using a second STM with an operating temperature of T = 6.5K. NRG simulations were performed with experimental broadening due to temperature and lock-in modulation taken into account.