It may depend on the fibres of the carpet. I have a large cream rug regularly cleaned, which is 100% wool and the only smell is damp wool for a couple of hours. The rug always comes up beautifully
Are You Finding the Hot Weather is Making you Short Tempered?



), but I don't remember there being any smell afterwards at all. I have an allergic reaction to most 'manufactured' perfumes, so I'm sure I would have remembered.
