"Reuter, m., ‘trooper,’ first occurs in early ModHG., formed from Du. ruiter, ‘trooper,’ which has nothing to do with reiten, ‘to ride.’ The word is based rather on MidLat. ruptarii (for ruptuarii), rutarii (ex Gallica pronuntiatione); thus were “dicti quidam praedones sub XI. saeculum ex rusticis collecti ac conflati qui provincias populabantur et interdum militiae principum sese addicebant”: “these people were often on horseback.” Thus Du. ruiter could easily acquire the meaning ‘horseman’; comp. Du. ruiten, ‘to plunder.’ See Rotte."
https://en.wikisource.org/wiki/An_Etymological_Dictionary_of_the_Ge...
"9 reuter, m. für reiter, vgl. sp. 777.
9 reuter, m. neben reiter, sieb sp. 780. 781: cribrum reutere Dief. 157b.
6 reutern, verb. für reitern, sieben sp. 784: cribrare reutern Di "