I am a hand quilter and use my quilts on a daily basis. They do not get rough treatment but they are not overly protected either. I put them through the washer and the dryer and they are holding up quite well. I would spot that stain with Dawn, let it set for a few minutes and put it in the washer if it were me dealing with this. If there are oils in whatever that is, Dawn will address that. I would not take it to a dry cleaner. How would you have handled this stain if it had been on a piece of clothing made from the same fabric? The fact of hand quilting is an aside--my opinion. It's all thread, just applied in a different manner. (I'm assuming the quilt is made of "cotton", not a delicate fabric such as silk or velvet.)
PS--I do not use fabric softener on my quilts--neither liquid or sheets. I'd rather rinse everything out of them and leave them "clean".