Does their quote mean any thing?

My next door neighbours go a quote to chop down some trees that divide our gardens but, we have paper work saying the trees belong to us but they said that when they are saying that they are theirs because we have a ditch on our side of the trees (I live in the country side) and they are going to ruin the house (they don't have any house insurance), first does the quote mean any thing and second could we take them to court if they did chop down the trees?