If you look at the image carefully there is a pro-tip from the manufacturer: "Use a screwdriver to take out the screws." Thanks Hoover, I couldn't have figured that out on my own. After unscrewing the screws with a screwdriver (who would have thunk?) the problem becomes clear:
Look at that big ugly piece of fluff, let's take that out. Hmm, there seems to be more stuck in. Ok let's take off the back hose and cram something in there to get it out.
Now we are cooking with gas. After I pushed as much as I could out with the stick, I pushed an old ethernet cable through so that the pokey plug in bit could grab any stragglers that were left behind.
Yikes that is a lot of fluff (and one lego, score!). Let's clean off the string/hair/thread before we put it back. Ah, that's better:
Now to reassemble and test and it purrs like a kitten.
I wonder what we'll do next week.