Sylvia Gonzalez, a 72-year-old city councilwoman in Castle Hill, Texas, was arrested in 2019 for misplacing a piece of paper after criticizing the city manager.

The charges were soon dropped. Ms. Gonzalez resigned and sued city officials, accusing them of retaliation for exercising her First Amendment rights.

But her case ran into the Supreme Court’s general rule that people cannot sue for retaliatory arrest, whatever the arresting officer’s motive, so long as the officer had enough evidence of a crime to support an arrest.

An appeals court dismissed her case. The judges said all that mattered was that Ms. Gonzalez had conceded that there had been probable cause for the arrest, for violating a Texas law making it a crime to conceal government records.

Ms. Gonzalez argued that it was a free-speech issue and that she never would have been arrested had she not spoken out against the city manager. The appeals court rejected that argument, saying she could not prove that she had been treated differently from others arrested for the same crime.

On Wednesday, a lawyer for Ms. Gonzalez urged the Supreme Court to let her try to prove that other people who had done what she was accused of would not have been arrested.