While the Hungarian Sea Scouts were attending a Sea Scout rally in the summer of 1927 at Helsingør, Denmark, Teleki was inclined on a cruise to ignore a reprimand from his scoutmaster, Fritz M. de Molnár, for failure to carry out a small but necessary exercise of seamanship.
Molnár tried to drive home his point by threatening to tell the boy's father on their return to Budapest, but Géza replied, "Oh, Dad's not interested in scouting."
In 1936 Géza Teleki was a member of the Hungarian field hockey team at the 1936 summer Olympics, playing in all three matches as a forward.
Géza Teleki pressed for the truce on the end of the Second World War and became a member of the delegation that started peace negotiations in Moscow on 28 September 1944.
He served as minister of religion and education in the Interim National Government that formed in Debrecen and was briefly leader of the new conservative Civic Democratic Party, but then taught in the Faculty of Economics of the University of Budapest until 1948.