Retrieving the farm animal is irritating? (7,4,4)

'irritating?' is the definition.
I know nothing about this answer so I can't tell whether this works.

'retrieving the farm animal' is the wordplay.
I cannot quite understand how this works, but
'the' could be 't' (the is pronounced as a 't' sound in some dialects) and 't' is found within the answer.
'animal' could be 'goat' (I've seen this before) and 'goat' is present in the answer.
This explanation may well be incorrect...

'is' acts as a link.

Can you help me to learn more?