I'm not sure what these stains are exactly but my best guess is water marks/stains from this time I left the windows open and blinds down, then it stormed.

Any idea what I might use to get them clean/stain free? Cleaning the slats was easy, but I haven't tried the cloth tape as I don't want to risk making it worse. The cloth is cottony feeling, so could be cotton or a cotton blend. The tape and slats are both white.