He was arrested by Gardaí at Cork Airport when the Paris flight landed and was taken to Togher Garda Station for questioning.
Judge Olann Kelleher was told by Inspector Finbarr O'Sullivan that the State was consenting to the defendant being remanded on bail in relation to the matter.
RTÉ denies the claims and has alleged Mr Gallagher damaged his own election prospects because of the manner in which he responded to certain assertions.
Ray Managh A Co Dublin couple, who claimed they had been defamed and falsely imprisoned at Dublin Airport after being questioned about an amount of cash one of them was carrying, have withdrawn their claims...
He said he hoped these could be answered by the end of the week.
Both sides agreed the matter could be adjourned to October.
The action arises out of a tweet read out by presenter Pat Kenny during the final televised debate of the campaign, prior to which Mr Gallagher was regarded as the frontrunner.
A Twitter account with a username similar to that of the official Martin Mc Guinness campaign, but not linked to Mr Mc Guinness, said a man who claimed he had given a €5,000 cheque to Mr Gallagher would appear at a press conference the next day.
However, Mr O’Callaghan said BSI had highlighted eight outstanding questions for his client.
Although the southern civil rights movement first hit the national headlines in the 1950s and 1960s, the struggle for racial equality in America had begun long before.
Indeed, resistance to institutionalized white supremacy dates back to the formal establishment of segregation in the late nineteenth century.
Community leaders in Savannah and Atlanta protested the segregation of public transport at the turn of the century, and individual and community acts of resistance to white domination abounded across the state even during the height of lynching and repression.
Atlanta washerwomen, for example, joined together to strike for better pay, and black homes often contained guns to fight off the Ku Klux Klan.