A Native American couple is claiming that the San Francisco Giants’ stadium-wide ban on “cultural insensitivity” does not go far enough.

The couple’s lawyer, Rachel Ledermen, is demanding that the stadium require cultural-sensitivity training for all security employees and forbid displaying team names such as “Braves” or “Indians” anywhere in the park.

Ledermen also demands that the existing policy against “cultural insensitivity” be updated to specify that it’s “including, but not limited to, Native American-themed headdresses and other appropriations of Native American culture and/or spirituality.”

Ledermen made the demands in a letter sent to the team on Monday.

The couple, April Negrette and Kimball Bighorse, first made headlines in June after they were ejected from the park following a confrontation with another patron who was wearing a headdress.

They filed a claim against the City and County of San Francisco seeking $10,000 in damages for the incident yesterday — and the Giants’ response to Ledermen’s demands will determine whether or not the team winds up listed on that lawsuit, too.

“That depends on the Giants’ response,” Ledermen said. “We’re giving them the opportunity to work it out.”

— Katherine Timpf is a reporter at National Review Online.