By Lemma 5.0.3, the retraction $\rho_{\mathscr{X}}$ over $\Star(\tau_{C})$ only depends on the formal completion $\widehat{\mathscr{X}_{/C}}$. By [Knu71, V, Theorem 2.5], since $C$ is a scheme, the formal algebraic space $\widehat{\mathscr{X}_{/C}}$ is a formal scheme. We are therefore in the setting of [NXY19, Proposition 5.4, Theorem 6.1] and we can conclude. ∎