to remove a website or a part of a website from the index (= list of contents) of a search engine so that it does not appear as a result of searches

You might want to de-index your website if it includes some outdated content that you plan to update later. 如果你的网站包含一些过时的内容，而你计划稍后更新这些内容，那么你可能需要从搜索引擎的索引中删除网站。

The search engine may temporarily or permanently deindex sites if they violate quality guidelines.

to remove the link between a pension (= a regular payment made to someone who does not work any more) or other benefit from a list of prices, so that the payment no longer increases when those prices increase

There were concerns that the regulations would be used to de-index pension benefits. 有人担心这些规定会被用来让养老金福利与介个指数脱钩。