Crossword Genius

A dog's upset the paint (9)

Ross

I believe the answer is:

distemper

I'm a little stuck... Click here to teach me more about this clue!

'paint' is the definition.
(I know that distemper is a type of paint)

'a dog's upset the' is the wordplay.
I cannot really understand how this works, but
'a' could be 'per' (eg 'one a day' means 'one per day') and 'per' is located in the answer.
'the' could be 't' (the is pronounced as a 't' sound in some dialects) and 't' is found within the answer.
This explanation may well be incorrect...

Can you help me to learn more?

(Other definitions for distemper that I've seen before include "Sickness" , "problem for dog ..." , "Water-based paint" , "Paint; disease of dogs" , "A way of painting" .)

I've seen this clue in The Globe and Mail.
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