Rude in food shop, provide grub not right (10)

I believe the answer is:
indelicate
'rude' is the definition.
(I've seen this before)
'in food shop provide grub not right' is the wordplay.
I cannot really see how this works, but
'in' is present in the answer.
'food' could be 'cat' (cat food is a kind of food) and 'cat' is found within the answer.
'shop' could be 'deli' (delicatessen) and 'deli' is found in the answer.
A single letter 'e' remains which might be clued in a way I don't understand.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for indelicate that I've seen before include "Coarse" , "Rather rude" , "Saucy" , "Practised (a play)" , "Rude - tasteless" .)
