if you are using the mobile version of facebook, that is, m.facebook
dot com, you should be able to go to that person's timeline and look
for the "block" button or link. I've only done that to a couple of
people, and there was a message about how blocking someone doesn't
always block someone all the way. they can't send you messages but I
think they can see you if you are following a thread of comments and
you both follow the thread. I wish I knew how to remove messages from
parts of facebook, but so far, I've only been able to remove posts
that I've made. I wish I knew how to get rid of the nonsense that's
associated with pics. It slows things down when jaws reads 20 or so
random number-letter tags. you'd think with all the technology for
facial recognition, facebook could automatically tag pics of cats and
dogs or children. Picture of cat. Picture of dog. Picture of child
playing in snow, etc. One of my friends has kindly been putting short
descriptions when he posts pics.

Other than reporting an offending message to facebook tech support
(does that exist?) and asking them to remove it, I don't know how
anyone removes messages from facebook.

Sorry