Isela Villalobos, of McAllen, Texas, was among relatives of Garza who appeared via satellite Tuesday on NBC's "Today" show.
Villalobos said Garza's mother, Elizabeth Ezquivel, had clung to her phone for 16 months after her daughter disappeared.
She turned it off for the first time on Friday, when she got the news. Villalobos said learning of Laura's death was "a really sad moment" for the grieving family.
Garza had moved to Brooklyn five months before she disappeared.
Garza was last seen in Dec. 2008 with registered sex offender Michael Mele. She vanished after leaving New York's Marquee Nightclub.
On April 11, 2010, more than a year later, kids on ATVs found skeletal remains in a field near Olyphant, Pa, about an hour's drive from where Mele lived. He has been investigated but not charged in the case.
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