A note on quasi-transitive graphs quasi-isometric to planar (Cayley) graphs

Given a connected, locally finite, quasi-transitive graph $X$ which is quasi-isometric to a planar graph $\mathrm{\Gamma }$, we remark that one can upgrade $\mathrm{\Gamma }$ to be a planar Cayley graph, answering a question raised by Esperet–Giocanti and Hamann.