A hearing is scheduled for 9:30 a.m. Aug. 10.
Bradford did not return an email seeking comment.
Davis also sent a letter to the store demanding that it stop selling dogs from breeders and instead convert to a shelter adoption business model. She said last week that she has not received a response to the letter.
"We have irrefutable evidence of the inhumane pet factories that supply her store," Davis said. "It will not work. I will not be intimidated and will continue to tell the ugly truth about I Heart Puppies."
Davis has warned that animal-rights groups are planning to protest the shop at 2801 E. Coast Hwy. Newport Beach police said they are aware that protests and pickets could be taking place in the near future.
Davis referred other questions to her lawyer, Bryan Pease, who said she has not been served by Bradford's complaint. Pease was also not clear whether a temporary restraining order was already in place.
He contended that Davis had not harassed the shop, however, and that in her actions she was within her constitutional rights of free speech.
"She's not harassing people," he said. "She's done this with hundreds of other pet stores. I'm 100% confident that she will prevail (in court), and the pet store will pay my attorney's fees."
Last week, the Corona del Mar Residents Assn. board declined to approve creation of a membership survey asking whether the Newport Beach City Council should create an ordinance banning the sale of non-shelter animals from local pet shops.
The Corona del Mar Business Improvement District board may discuss the issue at future meetings.
I Heart Puppies opened July 1 and almost immediately drew national scrutiny from animal-rights activists.