Take your litter home with you.The ambiguity is between what linguists call a 'strict identity' and a 'sloppy identity' reading of the missing bit of the second sentence. Others do stands for either Other people take your litter home with them or Other people take their litter home with them. The first one is the strict reading because it strictly preserves the part of the original sentence that is elided, and the reference is the sloppy one because it allows the reference to shift from your litter to theirs, along with the subject.
[Aside: note that the fact that the second pronoun must be them in either case, namely the sloppy reading. I'm not sure why; something about the semantics of take and home and you, probably. But it seems to be an exception to the generalisation discussed here by Neal Whitman, referring to work by Johnson and Dahl, that you can have all the possible combinations of strict and sloppy except for the one where the first is strict and the second sloppy. Which is weird.]
Unlike with most ambiguity, where context tells you which meaning is probably meant, I don't think it's so clearcut here. Presumably they are trying to shame you by saying that other people behave properly so you ought to as well (sloppy). But it is possible, I think, that it means that if you don't take your litter home, the litter-pickers will have to pick it up and take it away (presumably not literally to their homes), namely the strict reading. (We'll leave aside the point that if you take it home it's not litter, which is what my aunt Becky always points out.)
Right, I've gone on about this for so long I'm now completely unable to English so I'll do the other sign for a new post tomorrow.