An organic clothing store opened in my town and when I went to check it out I found the smell somewhat unpleasant but I assumed it was because the store was newly fitted out. When the smell was still there on a subsequent visit some time later I commented on it and I was told it was the smell of the silk in some of their clothes. I was assured that it washes out after about four washes.

I bought three or four items at various times and possibly one got the full four washes, which didn't completely remove the smell. I did some googling and read that good quality silk is processed in such a way that the smell is removed but cheaper silk basically relies on the purchaser eventually washing it out. At that point washing those items again and again was not a priority so I never have reached the point of making those clothes wearable.

Perhaps your tank hasn't been washed often enough yet, or perhaps even the previous owner got frustrated enough with the lingering smell that some desperate measures were tried which merely added to the smell?