I don't know of any sites besides imgur, but you might look into tools you can use yourself to clean images before uploading to them to some host that doesn't do that for you. That's actually even safer, because it means a third party never gets to handle that data in the first place. Not as convenient, though.
Thanks. I'm glad that someone didn't just tell me to do a google search. Maybe I don't know what I'm really looking for and in this case you suggested an alternative. I think adding a pip to your circle is like getting an upvote.
Unless someone is being really obtuse, I never tell anybody to just Google it, because I hate googling for things and getting nothing but posts where people ask the same question I have, and there's no answer other than "google it." I'm not gonna contribute to a problem that affects me.