“弄伤了背的”可以翻译为 “with a back injury” 或者 “who has injured their back” 。
例如：
The athlete with a back injury had to withdraw from the competition.（那个弄伤了背的运动员不得不退出比赛。）
The person who has injured their back is finding it hard to move.（那个弄伤了背的人发现很难移动 。）