The lids are held on with tie wraps (plus friction). With the increasing speed of canburglars, removed lids are likely to become more common. I don't see anything in the rules that would keep the RC from scoring, though only one litter score would be credited:
Quote:
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LITTER Scored in/on a RECYCLING CONTAINER: 6 per RECYCLING CONTAINER
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note that's per container, not per piece of litter.