It means very little, but thanks a lot (3)
I believe the answer is:
tad
'it means very little' is the definition.
The definition suggests a singular noun which matches the answer.
'thanks a lot' is the wordplay.
'thanks' becomes 'ta' (UK informal version of 'thank you').
'a lot' becomes 'd' ().
'ta'+'d'='TAD'
'but' acts as a link.
Can you help me to learn more?
(Other definitions for tad that I've seen before include "Little bit" , "Smidgen" , "Slight amount" , "Modest amount" , "Small bit" .)