The most common and most likely answer to this crossword clue is the 7 letter word SMUDGES
I've seen this crossword clue in The Daily Telegraph
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Buddy explains!
The straight part
We know that "dirty marks" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case dirty marks = smudges.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.
What does SMUDGES mean?
SMUDGES noun- A blemish or smear, especially a dark or sooty one.
- Dense smoke, such as that used for fumigation.
- A heap of damp combustibles partially ignited and burning slowly, placed on the windward side of a house, tent, etc. to keep off mosquitoes or other insects.
- (especially in the phrase "smudge stick" = "stick of incense") A quantity of herbs used in suffumigation.