Question

这个that是什么从句？

I think it's people in the background that are disturbing her.
我觉得是背景里的人打扰了她。

这个that是什么从句？

Answer 1

您好，I think it's people in the backgroun that are disturbing her. 中的 that 引导的是（定语从句）修饰 people；in the background 应该是（介词短语）充当（后置定语）修饰 people。句子的（宾语从句）的 that 被省略了。
I think (that) it is people [in the background] that are disturbing her.
定语从句引导词 that 可以用来修饰物，也可以用来修饰人，在从句中充当从句的（主语），而因为先行词 people 和定语从句 that are disturbing her 被（in the background）分隔开来了，所以感觉比较难理解。

Answer 2

that引导的宾语从句