What is meant by Remote Diuretics & Remote Vomiting?
"Remote" can mean distant/far away, often in space but also in time (as in, the "remote past"). In just the search results you included in your question it is fairly clear that these sources are using the word "remote" to mean (relatively)"far away in time" or simply "not recent."

For example:


  associated with remote diuretic use, therefore, diuretic effects were already washed off


Referring to diuretic use in the past, so there is not current diuretic effect but the secondary consequences are still present.

Note that these terms are quite uncommon in the literature, I get 21 results in Google Scholar for "remote diuretic" and 16 for "remote vomiting" and nearly all seem to be related to the specific context of hypokalemia.