All four were nabbed on October 7 as they were attempting to cross the Ichhamati River, which separates India and Bangladesh, the BSF spokesperson said.
The central agency claimed to have come across leads showing the involvement of a section of customs officers posted in the districts.
The report, which was submitted to the state Chief Minister Sarbananda Sonowal and was supposed to be forwarded to the Centre, also wants sealing of the entire Indo-Bangladesh border.
Whiile India had allowed export of goods from Petrapole, the largest land border port with Bangladesh, on June 7, the state government was demanding that truck drivers have to undergo self-isolation.
Unavailability of drivers to take cargo to Bangladesh and problems related to parking of trucks in Petrapole have led to the crisis.
The earthquake took place around 7.10 am and its epicenter was located at a depth of 55 km and a place 82 km southeast of Sohra, officials at the Regional Seismological Centre said.
The Indian nationals, mostly from the northeastern states, crossed the border through the three checkpoints on the borders with Meghalaya, Assam and Tripura.
Indian High Commissioner to Bangladesh, Riva Ganguly Das, had travelled up to the border and supervised the return of the Indians.
Official sources declared the battalion headquarters, its administrative base camp at Gandachara, and Karina border outpost as containment zones.
Will take a call after considering all aspects: West Bengal government on MHA letter on Indo-Bangla trade
The Centre during the day came down heavily on the West Bengal government for not allowing movement of essential goods through the Indo-Bangladesh border.
The BSF had sought to hand the man over to the Border Guards Bangladesh but as two rounds of meetings between them yielded no breakthrough, he was handed over to Tripura police.
The stranded truckers, mostly from Punjab, Haryana, Madhya Pradesh, Maharashtra, Odisha and Nagaland, alleged that the transporters have left them in the lurch and are not picking up their calls.
The middle-aged woman was intercepted by the BSF on April 2 when she was being pushed into the Indian side by some Bangladeshis with the help of the BGB.
Residents of Kathalchhari and Amtali villages along the border claimed the BGB personnel along with locals have tried to push the woman into the Indian territory from 3 different places since April 2.
The minister reviewed the security of the two borders on Thursday with BSF officials via a video conferencing and directed the force to ensure that no cross-border movement takes place.