I don't know what Greplin is doing, but indexing alone doesn't imply they cache your data somewhere. Although the index contains pieces of your text, you can't reconstruct it from the inverted index alone.
From usability standpoint, they have this google-instant-search-esque thing going where they produce instant search result with text as soon as you start typing.
So unless they are hitting the APIs of every provider you authorized to them and searching through them in near real time, they are storing the data.