I agree with you 100%, i'd never pick up a dirty tissue that weren't mine. Teachers make you pick up stuff now cause it's all about recycling and littering. I suppose it would have been alright if she asked you to pick up a wrapper or something, but not a dirty tissue, you're not a doormat. She could have picked it up herself. Then again you could have picked it up using another tissue and then put it in the bin. And you asked her to move politely, and when she didn't you just walked past, so you didn't do anything wrong. She gave you the detention cause she probably didn't feel respected.
If she gives you a dentention, just say that to her. If she still gives you one, get your parents to ring up and complain, even though you might think it's childish, atleast you won't get one haa. I would do that, not getting a detention when i didn't do anything wrong! :) x