The 19-year-old striker arrived at United on an initial eight-week trial last month, but a decision has been made to let him pursue opportunities elsewhere in the professional game.
Bray trained and played with United's U21s during his time at the club and registered an assist as they drew 2-2 with Fulham in the Premier League 2 last month.
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The teenage striker, who used to live in Rochdale before moving to Exeter, was given permission to head to United on loan from his local club, Willand Rovers, who are in the Southern Football League.
Bray only joined the Devonshire side this summer, having joined from another local side, Holsworthy. He is regarded as one of the top talents in the area, having featured for Devon U18s earlier in his playing career.
United's U21s currently sit 12th in the Premier League 2 table and are yet to win a match in the league this season, though they did defeat Carlisle in the EFL Trophy last month.
Mark Dempsey's side have drawn each of their last three league games 2-2, sharing the spoils in consecutive matches against Everton, Fulham and Liverpool.
United's U21s are back in action on Friday night when they host West Ham at Leigh Sports Village.