After thanking them twice, setter is going up to get straw mat (6)
I believe the answer is:
tatami
'straw mat' is the definition.
(I've seen this in another clue)
I don't understand the remainder of the clue.
Can you help me to learn more?
(Other definitions for tatami that I've seen before include "Japanese rush and straw matting" , "Jap. room matting" , "Jap. floor mat" , "Floor-covering" , "Japanese straw mat; a mat, it (anag.)" .)