Falkirk's education department told The TES Scotland this week it was "actively trying to resolve the situation" at St Mungo's High in the town.
The Roman Catholic school has been at the centre of unwelcome media attention since before Christmas after senior pupils petitioned the headteacher to have two members of staff removed.
Frank McCaffery, the head of chemistry, and Claire McKeown, a modern studies teacher, had set up home together after Mr McCaffery left his wife Sonia, who teaches English at the school. Their daughter Elena is the school vice-captain.
The council initially distanced itself from the affair, stating that "it does not become involved in domestic, marital or personal matters unless they impact on the delivery of the service to such an extent that it raises questions of personal professional responsibility in carrying out the remit of the post".
But the statement added: "If there were to be demonstrable evidence of a deterioration in the quality of education in St Mungo's High School as a direct consequence of this matter, the director of education would be actively working with school management, and in consultation with the Roman Catholic Church authorities, to find an acceptable resolution."
Hugh Lynch, the former rector, Mrs McCaffery and her daughter have since given interviews to the press. Mr Lynch is reportedly angry over the damage to the school's reputation for upholding the sanctity of marriage. Mrs McCaffery talked of a "horrendously unwanted situation" which forced her to face her husband and Ms McKeown. The local paper ran a story on Elena McCaffery headlined "I'm dreading going back to my school".
Mrs McCaffery says she wants her husband and Ms McKeown transferred.
The episode has proved a baptism of fire for Andrew Mimnagh, who took up his post as headteacher at the beginning of December but is considered to have handled the sensitivities well. Mr Mimnagh said in a statement: "I am aware that we should all be living witness of our faith to our children but I am also aware of human failing and the need for Christian charity when any of us fall below the high standards set by our faith. When anyone, whether parent, member of staff or child, has difficulties in their lives, as a school we are a support. We do not condone nor do we condemn."
Mr McCaffery and Ms McKeown have been relieved of their religious and personal and social education classes, a step which coincided with the arrival of the pupils' petition on his desk.
The affair represents a vivid illustration of the potential of pupil power, which was given prominence at a national conference in Aberdeen last November. A call from the city council's pupil forum for pupils to be able to express their views on the quality of teachers was endorsed by John Stodter, the director of education, and Archie McGlynn, chief inspector of schools.
But the Educational Institute of Scotland warned against a "popularity poll" among pupils to decide whether teachers were competent or not.