The demand was hand in during a protest against the continuing ban outside the Aberdeen offices on Wednesday organised by the UK's largest peace group network, Stop the War Coalition (STWC).
According to the Islamic republic news agency, local demonstrators carrying banners chant for Thompson to resign over continuing the ban in the face of widespread condemnation of his decision two weeks ago following Israel's latest massacres in Gaza.
"No one will come out and talk to us about the decision so we have been forced to stay outside and shout. What we are saying is that their decision not to show the appeal to protect their impartiality is unprecedented," said STWC member John Connon.
"We are threatening to continue with the protest at another time if need be," 53-year old Connon told the local daily Press and Journal in Aberdeen.
The Crisis Gaza Appeal was launched on behalf of 13 leading British charities by the Disaster Emergency Committee. It was broadcast by Britain's four other terrestrial channels, ITV, Channel Four and Channel 5, but not by Sky satellite station.
Elsewhere in Scotland, the BBC ban has been condemned by Liberal Democrat member of Edinburgh's devolved parliament, Hugh O'Donnell, who joined an aid mission to Gaza just weeks before Israel launched its latest onslaught at the end of December.
O'Donnell, who has volunteered to transport four Scottish doctors to help treat the injured in Gaza, insisted that it was not too late for the BBC to reverse its decision and broadcast the emergency appeal.
"People are smart enough to distinguish between an aid appeal for a growing humanitarian disaster and showing support for a political stance. The BBC should reverse their cowardly decision and show the appeal today," he said.
O'Donnell, who is MSP for central Scotland, is launching the aid mission under the banner of Doctors for Gaza, which is due to leave from Scottish Parliament on February 13 and will be joined by more vehicles before joining the main convoy in London.
Almost 190 MPs in the British parliament have also condemned the BBC's refusal, saying that its excuse that it would jeopardise its editorial impartiality as "unconvincing and incoherent."
Staff at the corporation have accused the BBC of being pro-Israeli by banning the humanitarian appeal.