As fun as it is to plot revenge, should this escalate you'll end up looking just as bad as she does. So by all means, I think we should absolutely all keep posting on here about the rank things we could do to her and her washing...
But here's what I would do, based on my interpretation of the information available:
It is not her space, and she has no right to use it. Presumably she had an "agreement", with whoever lived there before you, be it spoken or unspoken. They do not live there anymore, you do. Therefore, any agreement is rendered null and void.
You need to make it clear, verbally (and possibly even in writing), that you do not want her items on your line, and if she continues to put them there they will be removed. There's no need to be threatening or angry in this communication, just be very matter of fact: this is not your space, you do not have my permission to use it, so if you do use it, I will remove your items.
Then, if/when she continues to put her things there, take them down and leave them in a basket on the edge of your property. Wet or dry, no sense in you making the trip down there and saving her the hassle. She'll probably begin to expect it! Then not only does she not have to use her own line, she gets it unpegged and returned free of charge!
Leave the items in a basket, on your property, not folded, but not tampered with. If they are wet, so be it. If they sit there a while, so be it. If it rains, so be it. A vague disclaimer is nobody's friend, you made it clear what would happen, so if she chooses to continue this behavior she only has herself to blame.
Lastly, I wouldn't think you would need to bother with putting your own out (unless you want to). The message you are trying to impart is "you can't use it because I need it", because that can be countered with "well, you're not using it right now, so where's the problem?" The message you are trying to impart is, "it's irrelevant if I am using it right now or not, the fact is that you do not have permission to use it and I will not permit you to use it, period."