Greek character prodding a breeding dog? That’s uncalled-for (1,3,4)
I believe the answer is:
a bit much
'uncalled-for' is the definition.
(a bit much can mean uncalled for or unnecessary)
'greek character prodding a breeding dog?' is the wordplay.
'greek character' becomes 'mu' (letter from the Greek alphabet).
'prodding' is an insertion indicator (prod can mean to poke a hole into something).
'breeding dog?' becomes 'bitch' (female dog).
'a'+'bitch'='abitch'
'mu' going into 'abitch' is 'A BIT MUCH'.
'that's' acts as a link.
(Other definitions for a bit much that I've seen before include "Contradiction in terms" , "unfair" , "unacceptable" , "out of order" , "Butch ami may be excessive, beyond the limit" .)