Can you describe the support system allowing you to mount your green screen to a pair of stands?
And you mentioned washing one of them.
Naturally, wrinkles are highly undesirable. But your mounting system probably supplies tension sufficient to reduce the wrinkles to the point of negligibility.
Can you mention how you raised it up, and secured it? Were you using clamps, clothespins, or the equivalent? I can imagine some people riveting the green screen to a tarp that already has tethering rings. You probably didn't take it that far, but maybe you did?