The much-travelled full-back, 29, has been with the Fartowners for the last month and played in two games.
He scored on debut during the 38-6 win over Hull KR – Huddersfield’s only victory this term – and featured the following week against Catalans Dragons.
However, Tansey was not allowed to face parent club Wakefield on Good Friday and, with Giants having signed Leigh Centurions’ Ryan Brierley, was not selected for Easter Monday’s loss against Salford.
“Jordan is back now as a Wakefield player,” said Giants coach Paul Anderson, with the former Leeds Rhinos and Hull FC player now hoping to make a positive impression under Chris Chester who has taken over as Trinity coach since he moved on loan.
“With Jared Simpson back to full fitness, Ryan Brierley having played at full-back the other day and Scott Grix hoping to return around the time of Magic Weekend, we’ve got cover in that position.
“We’d obviously like to thank him for his time here.
“He was good for us and we’d like to think we were good for him.
“But there’s no point keeping him here if he’s not going to play, even though he is an experienced player.”
Ireland international Grix, meanwhile, has been out since the opening night after injuring his shoulder against St Helens.
However, the 31-year-old’s recovery is ahead of schedule and Anderson hopes he could be fit for the game against St Helens in Newcastle on May 22 which would be around a month earlier than first thought.
Former Bradford Bulls winger/full-back Jamie Foster is still training with Giants, although that is simply to keep fit and Anderson says there is no long-term future for the trialist at the West Yorkshire club.