The most common and most likely answer to this crossword clue is the 5 plus 5 letter word WHITE SHEET
W
H
I
T
E
S
H
E
E
T
Buddy explains!
The straight part
We know that "Might one see character ending contrite with these scruffy clothes?" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case might one see character ending contrite with these scruffy clothes? = white sheet.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.