In 1911, the Swiss artist Johann Bossard came across an empty property in the grasslands near this small town south of Hamburg. Inspired by the location, he purchased the land and together with his wife, Jutta, spent decades building his life’s great project: three esoterically shaped art-covered buildings and a landscaped garden. Since 1997, the site has been a museum known as the Kunststätte Bossard, and an off-the-beaten-path destination for fans of expressionist art and architecture.

But in 2017, Alexandra Eicks, an employee on the site, made a discovery that threw the project in a more sinister light. Ms. Eicks was preparing for a children’s art class when she noticed a geometric shape on the studio’s mosaic floor that nobody at the museum had seen before: a swastika. Because the tiles had been installed after the Nazis’ rise to power, it raised the possibility that the Bossards held more troubling views than had previously been known.

Three years later, the mosaic is at the center of a pointed debate in this pastoral corner of northwestern Germany. Activists are demanding the swastika’s removal, but the museum says the whole site is a “Gesamtkunstwerk” — a total work of art — that should not be altered impulsively, and that the symbol should stay so it can be used to educate visitors about the country’s past.

It has also prompted a broader discussion about what should be done with art created by Nazi sympathizers, and about whether an artwork’s cultural value should ever override Germany’s ban on Third Reich symbols.