Andrew Beech, 24, Christopher Fletcher, 30, and Lee Bates, 27, are alleged to have carried out the crime at a house in Bearsden last September.
The charge includes claims the trio pretended to be from the water board and entered the house by deceit and without permission.
It is alleged a 79-year-old man and a woman, aged 76, were assaulted.
During the incident, a hand was allegedly put over the woman’s mouth and she was told not to speak or move.
It is alleged the man was pushed, knocked to the ground and restrained.
Prosecutors claimed demands for £20,000 were made, the house was ransacked and they robbed them of a “quantity of money”.
Bates faces a separate charge of attempting to pervert the course of justice.
Lawyers for the trio pleaded not guilty on their behalf at the High Court in Glasgow.
Judge Lord Mulholland adjourned the case until a further hearing next month.