Your clothesline idea is a good one! Fresh air and sunshine do a lot.
I'd worry about a chemical smell that won't wash out - you don't want to cover it up; if the chemical is still there and you breathe it, or take it in through your skin, no telling what the long term affects might be.
I bought beautiful, new, expensive sheets at an estate sale that had been packed in a cedar chest with moth balls! What a combination! Repeated washings didn't do it until I tried hanging them on the line in the sun - that sure helped!
That also says something about expensive gifts - don't save them so someone can buy them at your estate sale after you die! USE them and enjoy them!