> someone hand drew and coloured a poster for beloved missing dog -- not a print out or photocopy -- and someone just took it because they wanted to collect them

I do think this is problematic, but I imagine that the owners would usually not retrieve/keep the posters anyway, so I'm not sure the issue is necessarily with the fact that an original is being taken like there might be with some other artistic creation (I'm not sure the owner would object to not getting the original back; the posters will probably just be discarded anyway).

My concern is more that if someone put a lot of effort into making these posters for the purpose of attracting people's attention in order to get their pet back, it seems problematic to take it without knowing for sure that the pet has already been found even if there are multiple posters in a neighborhood.