Aisha Ali-Khan, 34, had already pleaded guilty to encouraging Mohammed Afiz Khan,46, to obtain personal data relating to people she believed had sent e-mails on or about August 24, 2012.
Ali-Khan, who worked with Mr Galloway, the Respect MP for Bradford West, had asked Khan, then a detective inspector with the Metropolitan Police's counter-terrorism unit SO15, for help in finding out about some offensive material on the internet.
The couple, of Keighley, West Yorkshire, stood side-by-side in the dock in Southwark Crown Court, London, as the Recorder of Westminster Alastair McCreath sentenced them.
He told Ali-Khan: "I accept your criminality arises in circumstances where you were offended, and justifiably so, by someone putting material on the internet that was offensive to you.
"The request was unlawful. Whilst what you did was against the law, the request was understandable and led to nothing. Punishment as such is inappropriate - you must behave yourself for the next 12 months when this will be discharged."
Her husband, who had already pleaded guilty to two misconduct charges, was given a six-month jail sentence suspended for two years and ordered to pay £500 costs.
He was suspended from the Metropolitan Police after being charged in July last year and has been sacked.