As you know, fragrance-free washing powder is rarely found on the market today. My question is: What is the Islamic ruling if a woman goes out of her home while wearing clothes washed with fragrant washing powder, noting that those who pass beside her will smell the good smell of the clothes. Is such washing powder considered tempting to men; is a woman in such case included in the following Hadeeth?
"Any woman who applies perfume and passes by a group of people who may smell her perfume is an adulterous woman."

All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.

A woman is not permitted to go out of her home while wearing perfume. If the clothes washed with such washing powder have a fragrant smell that is detected by those whom she passes by, then it is impermissible for a woman to go out while wearing them except after removing the smell. However, if the fragrance is not so evident, then it is permissible for her to wear them. 

Allah knows best.