Recently, a worldsheet dual to free $ \mathcal{N} $ = 4 Super Yang-Mills has been proposed in terms of twistor variables for AdS$_{5}$, in parallel to that for the AdS$_{3}$ dual to the free symmetric orbifold CFT. In the latter case, holomorphic covering maps play a central role in determining correlators and are associated to Feynman diagrams. After recasting these maps in terms of the worldsheet twistor variables for AdS$_{3}$, we generalise to AdS$_{5}$. We propose stringy incidence relations and appropriate reality conditions for the twistor covering maps. For some special kinematic configurations of correlators, we exhibit an explicit construction of the corresponding covering map. We find that the closed string worldsheet corresponding to this map is related to a gauge theory Feynman diagram by the Strebel construction, as for AdS$_{3}$/CFT$_{2}$. Rather strikingly, the regularised Strebel area of the worldsheet reproduces the Feynman propagator of the free field theory.