The company has been forced to reduce its price, despite the fact that the offer has been very popular.

despite 是介词，意思是"尽管、虽然"，表示让步关系。 the 是定冠词，在这里特指后面提到的"事实"。 fact 是名词，意思是"事实、实际情况"。 that 是连词，引导同位语从句，用来具体说明前面提到的"事实"内容。 despite the fact that 是一个固定搭配，相当于 although 的用法，意思是"尽管...的事实"，用来引导让步状语从句。