The pair fled south after officials in Tarrant County, Texas, began an investigation into whether Couch violated the probation deal that kept him out of prison after he killed four people with his pickup truck in 2013.
Further details have come to light about Couch's time in Mexico, including an incident in which he ran up too big a tab at a strip club and was unable to pay, forcing his mother to foot the bill. The mother and son were arrested Monday after using a phone to order pizza delivery that was traced to a condominium complex in the Mexican resort city of Puerto Vallarta.
Tonya Couch is taken by authorities to a waiting vehicle after arriving at Los Angeles International Airport, Thursday, Dec. 31, 2015, in Los Angeles. She will remain jailed in Los Angeles until officers can take her to Texas, which likely won't happen until at least next week, Los Angeles District Attorney's Office spokeswoman Jane Robison said.
If the judge considering the appeal decides there was a mistake made in the process of detaining Couch, he could be released, and authorities would have to re-arrest him, Lopez said.
Authorities believe Couch's son fled to Mexico with his mother in November as prosecutors investigated whether he had violated his probation.
Federal authorities say Tonya Couch was flown to Los Angeles after she was deported from Mexico only because it was the most efficient way back to the U.S.
"We simply do not know when the Ethan and Tonya Couch will be returned to the USA", said Laura Vega, a spokeswoman with the service in Dallas. Authorities then launched a probe into a possible parole violation, law enforcement officials said.
Tonya and Ethan Couch fled to Puerto Vallarta, Mexico, as prosecutors investigated whether the 18-year-old had violated his probation.
The diagnosis is not recognized by the American Psychiatric Association and was widely ridiculed.
Ethan Couch was transferred on Wednesday to a migration facility in Mexico City where illegal immigrants are held while their cases are processed. His flight to Mexico rekindled anger over that sentence.
Richard Taylor is the acting U.S. Marshal for the Northern District of Texas. Her bond was set at $1 million.
Tarrant County Sheriff Dee Anderson commented on the delayed extradition in a tweet on Wednesday, saying, "Is anyone surprised the Couch duo are putting up legal fight to not return and face justice?"
NBC News has not independently confirmed a gun was found. The Tarrant County, Texas, District Attorney's office told NBC News it is looking into the report of a gun.
"Is there a chance that Ethan Couch could be successful in staying in Mexico?". Couch was convicted on four counts of intoxication manslaughter and sentenced to 10 years of drink and drug-free probation, which critics saw as leniency shown because of his family's wealth.