Rose crazy to come back with invite (6)
I believe the answer is:
damask
'rose' is the definition.
(damask rose is a kind of rose)
'crazy to come back with invite' is the wordplay.
'crazy' becomes 'mad' ('mad' can be a synonym of 'crazy').
'to come back' shows that the letters should be reversed in order.
'with' says to put letters next to each other.
'invite' becomes 'ask' (I've seen this before).
'mad' written backwards gives 'dam'.
'dam'+'ask'='DAMASK'
(Other definitions for damask that I've seen before include "Rich, heavy fabric with a pattern woven into it, a tablecloth say" , "Cloth, originally Syrian" , "Reversible fabric - type of rose" , "Lustrous cloth" , "Heavy embroidered linen" .)