Ethan Couch fled to Mexico in December with his mother after apparently violating the probation deal reached in juvenile court that kept him out of prison for killing four people in 2013.
Ethan Couch will return to Texas to face charges.
A Mexican federal judicial official said that Couch's attorney in Mexico filed a document on Sunday seeking to lift the injunction that has kept the 18-year-old in that country.
Ethan Couch's legal team presented a document to a court in western Jalisco state seeking to end the effort.
Tonya Couch is charged with hindering the apprehension of a felon and could face up to 10 years in prison if convicted. Ethan Couch is still being held in Mexico as he fights deportation.
Tonya Couch, madre del joven prófugo detenido en México, declaró que no puede pagar la fianza de un millón de dólares impuesta por un juez de Texas por ayudar a su hijo a escapar
Ethan Couch remains in custody in Mexico after winning a delay on his deportation back to Texas.
Tonya Couch, who was deported from Mexico last week, arrived on a flight from Los Angeles and was taken to Tarrant County Jail in handcuffs and leg irons.
El martes, un juez de Los Ángeles ordenó que Tonya Couch, madre del joven fugitivo detenido en México, regresara a Texas para que las autoridades locales determinen su situación
Según la agencia de noticias, Tonya Couch fue enviada en un vuelo de Guadalajara a Los Ángeles, pues, contrario a su hijo, ella no recibió ningún amparo