Tollen's reagent gives a positive test with aldehydes (and easily oxidisable groups). Hemiacetals (a carbon bearing both -OR and -OH on a ring carbon) exist in equilibrium with their open-chain aldehyde form and therefore reduce Tollen's reagent.

Structure C is a cyclic hemiacetal: ring oxygen and a hydroxyl group on the same carbon. It opens to an open-chain hydroxy-aldehyde, which is then oxidised by Tollen's reagent to give the silver mirror.

The methoxy-substituted analogues (A, B) and the simple tetrahydrofuran-derived structure D are acetals/ethers and do not undergo this equilibrium — no positive test.

$\therefore$ Compound C is correct.