Dr Pankaj Satija and his wife Dr Monika Ummat, both neurologists, have been working legally in the US for 15 years. They have a 7-year-old son and 4-year-old daughter.
The problem started when they visited India to see Dr Satija's sick father in October last year. On their return they were stopped at the Bush International airport by Customs and Border Protection officials because their travel documents had expired, the Houston Chronicle reported.
The Customs and Border Protection officials stamped their travel document saying that it would expire in June this year, when in fact the US Citizenship and Immigration Services noted that their document actually expired in June, 2016.
Upon returning to the US about a week later, a Customs and Border Protection official at the airport noted the discrepancy. The officials, however, allowed them to enter temporarily to correct the error.
On Wednesday, Dr Satija and his wife were abruptly told by immigration officials that they had 24 hours to leave the US. They were told that under a new policy, they could no longer extend their temporary permission to stay while they waited for permanent authorisation, local media reported.
The couple had called on their legislators and had taken the media along with their attorneys to plead their case. They reported, as ordered, to customs officials at Bush Intercontinental Airport, where they were told the agency had suddenly reversed course.
"Somebody at a higher level has made that decision," they were told by an agent. "I understand that you are physicians and a lot of lives are at stake."
The agency offered the couple three months of humanitarian parole, a rare measure allowing immigrants, who are otherwise not permitted to enter the US, the opportunity to do so due to a "compelling emergency" to sort out their paperwork.
"It was an unusual act of grace from an administration that has so far seemed intent on removing as many immigrants as it can, making few exceptions, even for those, like the Satijas, with good reasons to stay," the Houston Chronicle said in its report.