Integrating layered two-dimensional (2D) materials into 3D heterostructures offers opportunities for novel material functionalities and applications in electronics and photonics. In order to build the highest quality heterostructures, it is crucial to preserve the cleanliness and morphology of 2D material surfaces that come in contact with polymers such as PDMS during transfer. Here we report that substantial residues and up to ∼0.22% compressive strain can be present in monolayer MoS2 transferred using PDMS. We show that a UV-ozone pre-cleaning of the PDMS surface before exfoliation significantly reduces organic residues on transferred MoS2 flakes. An additional 200 ◦C vacuum anneal after transfer efficiently removes interfacial bubbles and wrinkles as well as accumulated strain, thereby restoring the surface morphology of transferred flakes to their native state. Our recipe is important for building clean heterostructures of 2D materials and increasing the reproducibility and reliability of devices based on them.