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Jones, competing in the -57kg category at the three-day series in Suzhou, China, lost 8-3 to Korea’s Sohee Kim.
There were also early exits for Britons Ruebyn Richards and Mike Harvey, who were beaten in the opening rounds of the men’s -68kg competition.
Jones, 21, tweeted later that she had had a “disappointing day”.
However, she still collected valuable qualification points towards the 2016 Olympic Games in Rio de Janeiro, Brazil, in the second grand prix event of the season.
The next grand prix is in Kazakhstan at the end of August, while the Great Britain squad will next compete in the Korean Open from July 11-16.
Jones, who won Great Britain’s first ever taekwondo Olympic gold medal at London 2012, had said she was in “confident mood” ahead of the tournament following victory at the Swiss Open in Lausanne last month.
Richards, 21, went out to Iranian Behnam Asbagikhanghah in a 9-4 second-round defeat.
He tweeted: “So gutted with that loss, didn’t feel anything like my sharpest towards the end of the fight, lessons to be learned in prep for Korea.”
Harvey, the 2012 European champion, lost 8-6 to world number 15 Hun Kim, of Korea, in the first round.
The three defeats on Sunday followed an otherwise successful grand prix for Great Britain, with bronze medals for Bianca Walkden and Mahama Cho.
masTaekwondo.com Team