To dispel an idea or feeling that people have means to stop

这个问题是这样的：
1.首先如果这句话你没有写错的话,应该是一个短语,不是句子.
分析：
to dispel an idea of feeling 是中心词,而that引导的句子是【同位语从句】即解释说明前面短语的
2.people have means to 可以翻译为【人们用手段（方法）去...】means可以翻译为方法,手段.
【举例】
to testify the fact that Diaoyu Island belongs to China
或：to testify the fact of Diaoyu Island belonging to China that Chinese have means to prove it.