meaning of "Like water off a duck's back"

[Salman]

Test No. express/advan-9 "Water Expressions", question 10

He'll be all right soon because any criticism is usually like water off a duck's back to him.

(a) of no importance
(b) of some importance
(c) of great importance
(d) of such importance

Test No. express/advan-9 "Water Expressions", answer 10

He'll be all right soon because any criticism is usually of no importance to him.

Correct answer: (a) of no importance
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Dear teachers,
Please, meaning of "Like water off a duck's back".

Salman

[Mister Micawber]

Because of the glandular oil with which they preen their feathers, waterfowl have plumage which repels moisture-- this is why they can swim about for a lengthy spell before getting too wet to float.

Water rolls off a duck's back without effect.
_________________
Canadian-American native speaker
who teaches English for a living at Mister Micawber's
ESL cafe: Interview with Mr. Micawber

[Lost_Soul]

Once I saw in a book this expression: like water off a duck's back with the article "the", i.e. like water off the duck's back.

Is the later expression also grammatical?
If yes, would you explain the difference, please?

thanks

[Mister Micawber]

.
'The' is grammatically fine but not idiomatic in your quote; it is referring to the duck of the idiom.
.
_________________
Canadian-American native speaker
who teaches English for a living at Mister Micawber's
ESL cafe: Interview with Mr. Micawber