The most common and most likely answer to this crossword clue is the 7 letter word MUDDIED
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Buddy explains!
The straight part
We know that "with grime cover" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case with grime cover = muddied.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 MUDDIED mean?
MUDDIED adjective- Made dirty with mud.
- Made unclear, obfuscated (generally as part of the phrase muddied the water)
- Made muted of color.
- To get mud on (something).
- To make a mess of, or create confusion with regard to; to muddle.