KnowYourPhrase.com - The Meanings and History For Popular Expressions
No further information is to be asked for beyond what was initially given.

Example: Everybody will have to use the bathroom upstairs, because the bathroom in the hallway is off limits today, 'no questions asked.' 
This expression has been around since at least the 1700s. An example of this phrase being used in writing comes from the Take The London Magazine from the year 1757, and there's a part inside that reads:

    "Whoever brings her to Mrs. Trolly's above-mentioned, or to the guard-room at E Whitehall, shall have fifty 
     guineas reward, and no questions asked."
* Bedtime for the kids will be one hour earlier than usual, no questions asked.
Note: The origins for many common idioms cannot be said with a certainty. In these cases, what may be provided instead is a theory as to how a phrase may have originated. No if theory is given, then I'll try to at least include a quote on the page to give you an idea for a old a phrase is, at minimum.

In addition, quotes that contain a phrase may be taken from old newspapers, poems, or books that were written centuries ago. If I quote a book from 1650 because it uses an expression, that does not necessarily mean the expression originates from this book. It simply means the saying is at least that old.
N-Letter Sayings  |  Know Your Phrase - The Meanings and Origins For Phrases and Common Idioms

N-Letter Sayings
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Phrases and Idioms