Triviality conjecture for the orientation double cover of string diagrams

Let $\mathcal{SD}$ be the space of oriented string diagrams and let $\mathcal{SD}^{\mathrm{u}}$ be the space of unoriented string diagrams. There is a double cover

$$\mathcal{SD}\longrightarrow\mathcal{SD}^{\mathrm{u}}.$$

Orientation-cover triviality conjecture. This double cover is trivial. The source does not provide a proof or status evidence for this assertion.