taken down a peg or two

Kotaro Isakaの小説 "Bullet Train" を読んでいます。

'But Tomoyasu's dad has some scary friends, or at least that's what Tomoyasu always says.'
'Ah, now that is annoying. Nobody likes to hear someone brag, but bragging about who you know is the worst. People who do that deserves to be taken down a peg or two.'

"taken down a peg or two" は慣用句でしょう。辞書を見ると "take down a peg" の項目がありました。

・Oxford English Dictionary: to make somebody realize that they are not as good, important, etc. as they think they are: He needed to be taken down a peg or two.
・Collins Dictionary: If you say that someone should be brought down a peg or be taken down a peg, you mean that they should be made to realize that they are not so important or wonderful as they think they are.: We thought it was time they were brought down a peg or two.
・Phrase Finder: To ‘take (or pull, or bring) down a peg (or two)’ is to lower someone’s high opinion of themselves.
Origin: Various quantities and qualities have been measured by the use of pegs. It has been suggested that the pegs in question here were those used to regulate the amount of drink taken from a barrel, or those that controlled the hoisting of the colours (flags) of ships. Either of these might be correct although, like the ‘yards’ of ‘the whole nine yards‘, ‘pegs’ could relate to many things.

動詞は "take" の他に "pull"、"bring" も使われ、"or two" も付けたり、付けなかったりするのですね。