don't worry about that的意思?

不要（为那事）担心。

别为某事担心、忧虑。
that后面引导的的宾语从句
I worry about that Tom will be late tomorrow.
我担心Tom明天会迟到。
Don't worry about that he won't catch up with the train.
不要担心他会赶不上火车。

还有，如果在下面对话中，don't worry about that中的that即不是引导宾语从句，只是指代之前所指的事物。
——I don't think I will pass the exam.
——Don't worry that.
(that 指代“考试不过关”这件事。）

别担心的意思。

别担心那事

别担心