When you delete the relay it should kick it off from your wiki relay list; is it not doing that?
The WoT filter is stored locally, it should be immediately persisted on every change you make
nostr:npub1l2vyh47mk2p0qlsku7hg0vn29faehy9hy34ygaclpn66ukqp3afqutajft
I changed the WoT-required score to 0 and deleted thesamecat relay, but I can't figure out how to save the changes.

When you delete the relay it should kick it off from your wiki relay list; is it not doing that?
The WoT filter is stored locally, it should be immediately persisted on every change you make
Neither element reacts persistently. When I reopen the panel, it is back to before.