The statue's permit was extended to February 2018.
But Di Modica has said he sees something insulting to the integrity of his artwork, saying "Fearless Girl" is not a symbol as much as a marketing ploy organized by State Street's advertising partner McCann.
While Di Modica says the bull's message is supposed to be "freedom in the world, peace, strength, power and love", his lawyers say Fearless Girl exploits the bull for commercial purposes.
"We believe that Mr. Di Modica's rights have been violated as a result of installing a statue of a young girl directly across from the Charging Bull", Siegel wrote.
This story has been corrected to show Modica will explain his challenge on Wednesday, not Thursday.
Displeased with that decision, Di Modica is fighting back.
Twenty-five per cent of the Russell 3000 - an index of the nation's largest companies - have no women on their boards, according to State Street, which manages many of their assets.
Attorney Norman Siegel holds an image showing the sculptures Charging Bull and "Fearless Girl" facing one another at his law offices in New York Wed., April 12, 2017.
He said a permit shouldn't have been issued and that the statue shouldn't have been installed without his permission.
"It's negative", Arturo Di Modica said of the girl's juxtaposition to the popular bull statue. The Italian immigrant intended the work to bolster American traders' spirits after the stock crash of a few years before - though the NYSE, it must be said, was not pleased with its holiday gift, hefting away the bull by the end of the day.
A spokeswoman for State Street Global Advisors did not immediately respond to requests for comment from Patch.
He put a finer point on the matter in a March interview with the New York Post and MarketWatch: "That is not a symbol!"
Siegel, former director of the New York Civil Liberties Union, said they did not intend to file a lawsuit.
His lawyers argue that proper procedure was not followed by city officials when choosing to grant the permit.
"There are some serious questions about how it was done", Siegel said.