Caveat: I do not actually have this seat although I have had other Britax seats and handled a lot of car seats.
The adjuster "loop" is usually just a long strap which is attached to the seat at the bottom end using velcro. Try giving a gentle tug on the bottom part of the loop and see if it detaches.
In any case, you shouldn't need to explicitly remove that strap because as you loosen the cover, it will slide through, and you'll also see how it's attached.
The manual is a bit confusing but I think what it essentially says is that you want to start with the cover of the headrest. So take the sunshade completely off, then undo the straps, remove the padding from the straps, which is velcroed on, then put the headrest up to the highest position and this should allow you to access the cover for the headrest.
It probably just slides off, but might be attached with hidden poppers under the cover, or Britax often use small loops of elastic which are attached to hooks. If it has this, and you can't get them off with your fingers, the handle of a teaspoon is usually helpful, or a biro with the pocket clip can be used as a hook. It can often be tight to get the first one off. IIRC it is pretty nerve wracking to try and remove the headrest cover the first time, because it feels too tight and like the polystyrene inside the headrest will snap. It should not snap as long as you are slow and gentle - don't bend it too far, but if you're overly worried about this then you're probably being too delicate!
Once you've detached the headrest cover, it says to push the headrest down all the way again, which probably makes it easier to loosen the rest of the cover. There are two poppers just behind the two seatbelt guides in front of the handle on the sides, and the other four poppers might be hidden under the padding. It also sounds like there is some velcro - I'd undo the poppers you can find, and run your hand around the edges of the cover to see if you can find this. There are also some loops (probably elastic) around the belt guides - again remember the teaspoon!
Getting it back on is essentially doing the same thing but backwards, so it might help to get someone to record you doing it so you can see what you've done. Teaspoon is useful again for any elastic loop hooks and also for tucking bits of cover behind plastic if there are any places where it's like that.
If you get stuck, Britax's helpline is good or they answer emails (potentially with a video) after a couple of days, or take it back to the place you bought it from if not online, and they should be able to show you.