This claim must be in error, because movie elements have already been seen in DSC. The show uses Marc Okrand's Klingonese, which was invented for ST III. The movie pronunciation "Kronos" for "Qo'noS" has been used in the show, by Mirror Georgiou; they're just variant romanizations of the same place name anyway, like Moscow/Moskva.
Earth Spacedock from ST III was seen under construction in Earth orbit in the season finale. Also in the finale, Ceti eels were glimpsed in a frying pan in the Orion sector of Qo'noS. The Starfleet ship designs are heavily movie-influenced, especially the Enterprise. Discovery's own design is based on a rejected Enterprise redesign from an abandoned 1976 feature film project. There's a starship named the T'Plana-Hath, after the philosopher mentioned in ST III.