Officials in Bavaria have suggested that the criticism is unfair.

“The Bavarian Ministry of Culture and state collections and institutions are committed to vigorous provenance research with the goal of rectifying injustices of the Nazi era,” Bavaria’s minister of art, Ludwig Spaenle, said last week after another settlement with Jewish heirs was reached.

Klee painted “Swamp Legend” in 1919, while living in Munich, and it is believed that Ms. Lissitzky-Küppers’s husband, Paul Küppers, acquired it there directly from the artist. In 1922, though, Mr. Küppers died of tuberculosis, and his widow met and fell in love with the Russian Constructivist artist El Lissitzky, whom she followed to the Soviet Union in 1926 and married a year later. On emigrating, she left her art collection of 16 paintings and one sculpture on loan to a German museum, the Hanover Provinzialmuseum — including works by Kandinsky, Piet Mondrian and Fernand Léger, as well as “Swamp Legend” and two other Klee pictures.

These artworks were among more than 20,000 seized from German museums in the virulent crusade by the propaganda minister Joseph Goebbels against art that the Nazis, no fans of abstraction or other Modern touches, perceived as “degenerate.” “Swamp Legend,” in particular, was scorned in the Munich “Degenerate Art” exhibition of 1937 as the product of the “confusion” and “disorder” of a “mentally ill person.”

It was soon purchased, though, by Hildebrand Gurlitt: the father of the reclusive Cornelius Gurlitt, whose secret art hoard in Munich was confiscated by German customs officials in 2012. The elder Gurlitt was one of just four dealers permitted to purchase the art the Nazis hated.

The trail of “Swamp Legend” was then lost until 1962, when it was sold at auction in Cologne. After two more changes of ownership, it was acquired jointly by the city of Munich and the Gabriele Münter Foundation in 1982.

Image The Museum Lenbachhaus in Munich. Credit... Stephan Goerlich for The New York Times

Ms. Lissitzky-Küppers tried in vain to reclaim her collection after the war. Banished to Siberia under Stalin because of her roots in hostile Germany, she died in poverty in Novosibirsk in 1978.