When Jessica Garcia decided to take her family’s 8-year-old chihuahua, Skippy, for a walk last week, she automatically headed south from her Springville Road home, knowing there would be fewer cars in that direction, making their path safer—or so she believed.But about 20 minutes into their early afternoon walk, shortly after the Hampton Bays resident turned onto Rampasture Road, both were confronted by a pair of American Staffordshire terriers, a breed commonly referred to as pit bulls. The dogs—later identified by authorities as Bandit, a 4-year-old female, and Bramble, a 2-year-old male, and who have a reputation of escaping from their nearby home on Cedar Lane and attacking smaller animals—were not on leashes and immediately ran toward Skippy.Both latched onto his tiny neck nearly simultaneously, killing him instantly, according to Skippy’s distraught owner.“The first time he bit my dog, I knew it … I knew he killed my dog,” Ms. Garcia said during an interview a few days after the incident, which occurred at around 1:30 p.m. on January 30, though she was unable to say which of the pit bulls attacked her family’s dog first. “I knew it the first time.”Through tears, she recalled how Skippy’s approximately 8-pound body immediately went limp on the end of his leash, the fresh gashes in his neck spurting blood that still stains the jacket and pants Ms. Garcia was wearing that day.She also noted how a man—later identified as the longtime dog-sitter for Bandit and Bramble, according to the dogs’ owner, Dayna Corlito of Hampton Bays—tried in vain to pull the two pit bulls off Skippy.“My dog didn’t move, he didn’t bark—[they] just attacked him,” Ms. Garcia said. “They just ran to attack my dog in front of me.”The image of two much larger dogs attacking Skippy—along with a series of other memories: calling her husband, Carlos, so he could help retrieve Skippy’s bloodied body from the street; carrying Skippy home in her arms; and then, finally, having to break the news to their children, Max, 12, and Charlie, 10—continues to haunt her.The family, who had raised Skippy since adopting him as a puppy, buried him in their backyard that afternoon, she said. “They’re sad,” Ms. Garcia said of her sons. “They are missing him a lot.”Ms. Corlito was cited in last week’s attack for violating a Southampton Town Court order—the result of an earlier attack involving the two animals.She said she decided to allow a veterinarian at the Southampton Animal Shelter in Hampton Bays to euthanize Bramble and Bandit on Sunday, five days prior to a scheduled court hearing on the violation, scheduled for Friday.Donald Bambrick, the town’s animal control supervisor, confirmed on Monday that both pit bulls were euthanized over the weekend. He also noted that Friday’s court hearing in Hampton Bays will go on as scheduled, explaining that they have to follow proper procedure in case the victims of such incidents opt to seek monetary damages.While she says her family will not seek monetary damages, Ms. Garcia said she intends to attend Friday’s hearing to demand that the courts prevent Ms. Corlito from adopting another potentially dangerous dog again.Ms. Corlito had been ordered by the courts last year to pay the veterinarian and personal medical bills of another Hampton Bays resident, Joanne Caton, after both she and her shih tzu, Sparky, were attacked by Bramble and Bandit on Rampasture Road in June 2016.Ms. Caton shared that Sparky was attacked in the same manner, with the two pit bulls essentially attacking him from both sides, repeatedly biting the small white dog on its neck and torso. The gashes required 10 stitches to close, and Sparky has also undergone multiple surgeries to repair injuries to his neck, according to his owner.Ms. Caton, meanwhile, suffered a sprained ankle and bruising on both her arms and legs—injuries she sustained while trying to fight off the two larger dogs that had escaped from their nearby home in the June incident. Her injuries left on her crutches for the better part of a week.As part of that court settlement, Bandit and Bramble were supposed to be confined to their backyard and, if they did manage to escape again, would be taken from Ms. Corlito.“It’s a big loss on both sides,” Ms. Corlito said on Monday, the day after her dogs were euthanized. “I’m having such a hard time with it myself—I’m sorry both families had to experience such a loss.”She added that her longtime dog-sitter, Jeffrey Peterson, who had unsuccessfully tried to pry to Bramble and Bandit from Skippy, also is distraught over the incident. Though he declined through Ms. Corlito to be interviewed, she said Mr. Peterson told her that Bandit, the larger of the two dogs, escaped when a clasp broke while he was trying to bring the animal to the backyard. It was unclear how the second dog managed to escape from the home.“Jeff is traumatized and still in shock,” Ms. Corlito said. “He’s just clearly heartbroken, too.”Carol Carlson of Hampton Bays said she was driving on Rampasture Road when she spotted the two pit bulls attacking Skippy. She said she immediately called Southampton Town Police from the safety of her car and waited for authorities to arrive. An officer with Southampton Town Animal Control was the first to arrive, followed by two Town Police officers, according to Ms. Garcia.Ms. Garcia said she was shocked when police told Mr. Peterson to bring the dogs back to their home as she was clutching her dead dog in her arms. “He took the dogs back home,” Ms. Garcia said. “They didn’t take them away.”Less than 24 hours later, both Bramble and Bandit were handed over to the Southampton Animal Shelter, and later euthanized.When reached this week, Ms. Caton, who spends the winters in Arizona, said she could not believe that the pit bulls had not only managed to escape but had attacked another dog. “When I heard [about] it, I got very upset because of the fact I remembered what I went through,” she said.Ms. Caton, who previously noted that she no longer walked her dog near her Hampton Bays home because of Bramble and Bandit, said their deaths came as a relief to both her and many of her neighbors. “I’m thrilled,” she said. “I’m so thrilled I can walk the neighborhood and not be afraid.”The June attack is not the only earlier incident involving the two dogs. In 2014, Bramble and Bandit reportedly injured another dog brought to Ms. Corlito’s house to play with her pit bulls. In a prior interview, Ms. Corlito said both the man and his dog were injured in the altercation, and that she agreed to pay the individual’s medical and veterinarian bills; the incident was never reported to the authorities, she said.As for Ms. Garcia, she said her family is still recovering from such a shocking and sudden loss, though she can at least take some comfort in knowing that the two pit bulls no longer pose a threat to other pets or even children who attend the nearby Hampton Bays Elementary School.“What if kids are playing and the dogs come?” she asked. “They will attack them too.”The Garcias have not yet decided if they will adopt another puppy in the near future. For now, they are still trying to get accustomed to a much quieter house, explaining that Skippy is no longer around to bark at passing cars, or to offer a warm greeting whenever they return home.“After work, he was more happy to see me than my kids,” Ms. Garcia recalled this week. “He was always jumping, and jumping and jumping—I miss him so much.”