I recently received some used coffee plungers, one of which looked like it may have been left for a very long time without being emptied - the filter mesh was black, it looked like it had been painted! This did not scrub off with a brush, and I thought it was completely ruined.
I ended up soaking it in a strong mix of dishwasher detergent - it took two soakings of about 30 mins, but the gunk was completely removed. I wish I had taken a before photo so I could show how well it worked, but I honestly expected it to fail and to throw it out.
This is worth keeping in mind for anyone who has a filter they are having trouble cleaning.