The family's attorney sent a letter with their demands last month. Neighbors said the dogs belong to NFL player Trent Williams.
Linda Flowers told ABC13 her 3-year-old lab mix went outside for 10 minutes one afternoon when it was attacked by Williams' dog at the fence line.
"We're being held captive in our own home," she said during an interview with ABC13 on Monday.
A wrought iron fence separates the property, and Flowers thinks the dogs were able to grab the dog named Sandy and pull her under the fence.
"My whole intent for this is that I want the dogs out," said Flowers. "They don't belong in this community, in a residential community, with families. The fact that there are more than four dogs, the legal limit, is a concern for us."
Flowers' attorney claims Williams has approximately between 10 and 12 Pitbulls at his Missouri City property.
According to court documents, after Williams was notified of Sandy's death, he allegedly said the dog "died like a b****."
The lawsuit alleges Williams made a dog kennel in his backyard without proper authorization and claims he's breeding and kenneling the dogs for profit through Instagram under the business name "Silverback Bully Gang."
The Instagram page describes the pet service as "an up and coming Texas based bully kennel for XL and XXL exotic tri color and Merle bullies."
Neighbors told ABC13 last month the dogs are known to roam the streets, leaving them terrified.
SEE ALSO: Neighborhood left terrorized after dog was mauled to death
Flowers fears a person could be attacked next.
"That it's going to happen to my children, that it's going to happen to a small child, even an adult," said Flowers.
ABC13 has reached out to Williams for comment. He has not returned our call, but he previously said one of his dogs was being attacked by Sandy and that the other dogs were merely protecting that dog.
That's something Flowers says isn't true.
"For Sandy to attack his dog is just completely ridiculous," said Flowers.