Lawyers given access by a judge said the children which had been held for weeks were "severely neglected".
One of them told the BBC that children were "locked up in horrific cells where there's an open toilet in the middle of the room" where they ate and slept.
The separation of migrant children from their parents began in 2018 under a new "zero tolerance" policy from President Donald Trump's administration. It saw nearly 3,000 children separated before it was suspended.
Under the policy, announced in May 2018, those who cross the border illegally were to be prosecuted - which required their children to be taken into care.
The border patrol in Texas reported the deaths of seven migrants this week who had apparently attempted to
circumvent the immigration system - including two babies and a toddler.
"There was nobody taking care of these children... they were not being bathed on a regular basis," Prof. Warren Binford of Williamette University in Oregon told the BBC after visiting the Clint facility in Texas.
"Several hundred of the children had been kept in a warehouse that was recently erected on the facility grounds.
"The cells are overcrowded... there's a lice infestation there, there is an influenza outbreak. Children are being locked up in isolation with no adult supervision, who are very, very ill and they're just lying on the ground on mats."
Elora Mukherjee, another lawyer who visited the facility, said: "They were wearing the same dirty clothing they crossed the border with. It is degrading and inhumane and shouldn't be happening in America."
In a statement, the border authority acknowledged that the Clint facility was not suited to the task.
The agency said it had moved children to more suitable facilities as soon as space was available.
On Monday, Democratic Representative Veronica Escobar, who had been deeply critical of the reported conditions, said she was told that only 30 children remained in the Clint facility.
There are limits set by the US authorities on how many people can claim asylum each day, resulting in a waiting period that can last months.
( With inputs from IANS )