I would like it thinned out this time.

would like 意思是“想要；希望”，属于“意欲动词”。 it 是宾语，过去分词 thinned out 作宾补，宾语和宾补是被动关系。

意欲动词 want, like, wish, expect, would like 等可以接复合宾语，过去分词作宾补。

I’d like the job done when I come back from the journey. 当我旅行回来时，我想让这工作（被别人）做完。

The father wants his daughter taught music in her free time. 父亲想让女儿在空闲时间学音乐。

上述动词也可以接不定式的被动式，作宾语补足语，即在过去分词前加 to be。例如：

They would like the book (to be) published this year. 他们想要这本书今年出版。

We want this matter (to be) settled immediately. 我们希望这个问题立刻被解决。