What is the derivation of the word "toetw", which is used in crossword puzzles to mean "a lightly scented perfume"?

It seems you found this here:

https://www.crosswordgiant.com/crossword-puzzle/53614/New-York-Times/2013-12-19

If you look closely, the listing of answers shows several "W". These are meant to mean "WATER". (WSKI, ICEW, SEAW).

It was likely a special crossword that excluded certain letter patterns or a messed up transcription as the list also includes "ETVOA" for "Cry at an unveiling", which would obviously be ETVOILA.

If we add back the missing IL, AT and ER, we get TOILETWATER.

Agree with the answer, but just want to add that the puzzle is about "oil" and "water" going together, in which O can be "oil" and W can be "water". So TOETW, adding in the oil and water, becomes TO[il]ETW[ater].