A teen fugitive from Texas known for using an "affluenza" defence was granted a three-day delay in deportation on Wednesday, but his mother was sent back to the U.S., according to a Mexican official.

Tonya Couch was put on a plane to Los Angeles because there were no more flights available to Texas. In Los Angeles, she was to be handed over to the U.S. Marshals Service, the official told Reuters.

Meanwhile, Ethan Couch, 18, remains in Mexico and a legal injunction filed to delay his extradition is still being processed. 

Both Couch and his mother had been scheduled to fly back to Houston on Wednesday evening after authorities said a phone call for pizza led to their capture in the Mexican resort city of Puerto Vallarta.

They were being held at immigration offices in Guadalajara.

Couch's attorneys did not immediately return calls for comment.

Return of Couch not imminent

A U.S. Marshals Service agent tipped local authorities off Monday to the location of Couch and his mother, according to a police report issued by the Jalisco state prosecutors' office.

Ethan Couch was on juvenile probation after killing four people in a 2013 drunken-driving wreck. He disappeared as authorities investigated whether he had violated the terms of his probation.

During the sentencing phase of Couch's trial in Texas, a defence expert argued that his wealthy parents coddled him into a sense of irresponsibility — a condition the expert termed "affluenza."

The condition is not recognized as a medical diagnosis by the American Psychiatric Association, and its invocation drew ridicule.

Mexican police say the fugitive "affluenza" teenager and his mother spent three days in a rented condo at a resort development in Puerto Vallarta before finding an apartment in a less glitzy area where they were found by police.