I don't see the issue here.
One of the
definitions of the word
mischief is "harm or trouble, especially as a result of an agent or cause". I think that is entirely in line with the intention of the sentence, saying "Trolls purses are the trouble". I think Tolkien just used what to us appears to be an unconventional manner of speaking (as he does through much of his works!), though it's entirely clear and correct from a grammatical view.