Filou has done that before and of course it needs lots and lots of work.
First - washing everything that has been in the laundry basket (and I'm sure you've done that).
Second: cleaning the basket itself, thoroughly and with the help of cleaning stuff. I think in the US there is some stuff that's called Nature's Miracle or so that seems to work really well.
Third: make sure there is no cat pee left over behind it or outside or under it. A black light can help to detect all traces of the smelly stuff.

If after all that it still smells I would suspect the basket has been used again Worst case could mean a new basket.

If it happens more than one time (Filou did it when my mom's dog was here) the kitty should be checked- could be an infection.