This is timely, because I just bought a lovely older scarf on eBay that REEKS of perfume (it's an orange and brown Les Coupes). It's terrible. I happen to despise perfume, but I think anyone would find it unbearable. Just being near it gives me a headache.
After a few days of airing it out did nothing, I washed it in cold water with The Laundress per instructions on this thread (thank you, posters!!). The water turned slightly orange, but no runs onto the white areas. Still smelled terrible. Repeat, still awful.
Since I can't wear it unless I get the smell out, and couldn't resell it in good conscience, I soaked it in cold water and vinegar (I think about 1:3 vinegar to water) for as long as I could stand (only about 3 minutes because I was worried about the colors). Then rinsed in cold, then repeated the process. The smell was better, but still very noticeable. So, I went for broke and washed it in warm soapy water. The water turned really orange, but it was in constant motion for only a moment, and it rinsed clear. I soaked it in cool vinegar water for 15 minutes, swirling every few minutes. Just finished ironing it, and the smell is MUCH MUCH better. Colors like fine - if there's any fading, I can't tell.
The hems are drying now and I hope I didn't just acclimate to the perfume. Even if it still smells, I think I'll be bold about washing my other scarves now, even the older ones.