I like the lactone suggestion a lot (I'll actually have more to say about that later), but surprisingly the authors don't form the lactone. Rather, like stewie mentioned, the TMS group is removed to give the free OH. As Heory mentioned, in this manner the structure is set nicely for an intramolecular hydrogen bond.
The hydrogen bonding stabilization turns out to be quite solvent dependent. The use of nonpolar, aprotic solvents encourage intramolecular hydrogen bonding, but polar protic solvents break up hydrogen bonding. Thus, even with the OH deprotected, running the photocycoaddition in methanol still gives a >25:1 dr for the undesired product. THF gives 7:1 dr, and hexanes gives 1.1:1 dr... in all three cases still favoring the undesired diastereomer.
So we're getting less worse selectivity, but still not selective. This does follow the order the authors describe in the paper. At this point, the authors modify the structure once more (again, not changing stereocenters) to try to favor the desired diastereomer even more. Act III: what is one more possible structural variation we could do to try to boost our dr in the right direction? (no, it's not lactone formation)