Tasty? No thanks, it's filthy! (3)
I believe the answer is:
sty
'it's filthy' is the definition.
I can't tell whether this definition defines the answer.
'tasty? no thanks' is the wordplay.
'no' suggests deleting specific letters.
'thanks' becomes 'ta' (UK informal version of 'thank you').
'tasty' with 'ta' taken away is 'STY'.
Can you help me to learn more?
(Other definitions for sty that I've seen before include "Pig pen" , "Pig home or eye sore" , "Porcine pen" , "Farmyard enclosure" , "Pig house" .)