Gomez Gonzalez's shooting Wednesday drew international attention after a bystander posted video of the aftermath on Facebook Live, showing her lying on the ground, bleeding.
Authorities changed their account of the incident,
adding to the controversy at a time when the White House has cracked down on illegal immigration.
The deadly encounter ended the journey Gomez Gonzalez started nearly three weeks ago in an indigenous community in San Juan Ostuncalco, Guatemala.
Family demands answers
Gomez Gonzalez earned a degree in accounting two years ago, but had not been able to find a job.
"She looked, looked and nothing," her father, Gilberto Gomez, said. "I believe that's the reason why she decided to pursue the 'American dream'."
The lack of job opportunities frustrated her, and she decided to leave her home and head to the US to find work. She was following the footsteps of her boyfriend, who made the same journey about a year before.
The 20-year-old had been traveling for over two weeks with other migrants when they were met by a Border Patrol agent in a residential area in the town of Rio Bravo, Texas.
The agent -- a 15-year veteran -- fired one round from his service-issued firearm, fatally wounding Gomez Gonzalez, the United States Customs and Border Protection said. The agent, who has not been identified, remains on administrative leave.
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In between sobs, her mother, Lidia Gonzalez Vasquez , said she only wants her daughter's body back.
"My girl did not go there to steal, my girl left to move forward and go to school," she said.
Her family held a news conference in Guatemala on Friday and asked for justice.
"It's not the first time someone dies in that country (United States)," her aunt, Dominga Vicente, told reporters. "There are many people who have been treated like animals and that isn't what we should do as people."
Representatives with Guatemala's Ministry of Foreign Affairs met with some of her relatives Friday to discuss the repatriation of her remains.
"Guatemala condemns violent acts and any other use of excessive force by the Border Patrol. We urge authorities to respect the rights of our citizens, especially their right to live, regardless of their immigration status," the ministry said in a statement.
Officials change story
Two days after the shooting, Customs and Border Protection revised its account of the incident, leading to many questions about what actually happened.
It initially reported the agent responded to a report of illegal activity on Wednesday and was attacked by migrants armed with "blunt objects." In its latest version of events, the federal agency makes no mention of any objects and only indicates the group "rushed" the officer after ignoring orders to get on the ground.
Additionally, the Border Patrol at first reported that a round from the officer's gun "fatally wounded one of the assailants" but the latest statement refers to the gunshot victim as a "member of the group."
A lot of details on the shooting have not been made public.
The federal agency canceled a news conference on the shooting and instead released its updated statement. An agency spokesman declined to comment further, saying the shooting was being investigated by the FBI and the Texas Rangers. An FBI spokesman declined to comment, citing an ongoing investigation.
'No reason to shoot a girl like that'
Marta Martinez, who recorded the aftermath of the shooting on her cell phone and posted videos on Facebook Live, was getting ready to attend her son's award ceremony at school when she heard a gunshot.
She ran out of her home and saw an officer turn over the body of a young woman.
The woman, Martinez said, was face-down in the ground but her face was covered with dirt on one side and blood on the other.
"I don't think there was no reason to shoot a girl like that, not even in the head," Martinez said.
In the video, a uniformed man is seen giving someone on the ground chest compressions but Martinez said the woman appeared to be dead.
In a vacant lot near her home, Martinez said an agent captured two men who ran from the scene after the shooting. She said she heard the officer tell the men: "This is what happens. You see?"
Agents arrested three undocumented immigrants, according to Customs and Border Protection.
In her video, Martinez can be heard yelling in Spanish at the officer who led the men to his vehicle: "Why do you mistreat them? Why did you shoot the girl? You killed her. He killed the girl. She's there. She's dead. I saw you with the gun, bro."
Rio Bravo is about a mile from the border with Mexico, and 170 miles south of San Antonio.