The most common and most likely answer to this crossword clue is the 5 plus 7 plus 2 plus 2 letter word THINK NOTHING OF IT
I've seen this crossword clue in The Times
T
H
I
N
K
N
O
T
H
I
N
G
O
F
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T
More clues leading to the result THINK NOTHING OF IT
Buddy explains!
The straight part
We know that "That matters not a bit!" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case that matters not a bit! = think nothing of it.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.