Yes it does make sense. I had exactly that problem last April when I wanted to wash it for baby no 2.
The tightener is stitched but the plastic hole it goes through in the front of the seat isn't completely divided (it looks like the strap threads a bit like a buckle) - you can push the strap through the middle of the hole to release it. In the end I found it much harder to get it all back on again and if I hadn't have had 2 identical seats then I'd still be trying now!
I realise that this may still not make sense but, if you haven't already worked it out, feel free to come back to me.