When does the DMG trigger of Ruined Rex. Let's say opponent Ruined Rex dies, I react with Thrill of the Hunt and try to invalid the target, does that work? And if not when is the timing to do so

Yes — Thrill of the Hunt works, provided you play it while Ruined Rex's Deathknell trigger is on the chain and before it resolves.

Here's the flow: Rex's [Deathknell][>] Deal 4 to an enemy unit goes onto the chain as Rex dies during the Combat Cleanup, an enemy unit is locked in as its target, and the trigger only actually resolves after the cleanup's heal step. You respond to that chain item with Thrill of the Hunt: it banishes your unit, and when its owner replays it, it enters as a new game object (Rule 124). The trigger's already-chosen target is gone, so the "deal 4" instruction is ignored (Rule 359.3.e.5 / FAQ #9870) — your unit takes nothing.

On the timing question: there's no window before the target is picked, because Rex's death happens inside the cleanup task itself. Your window is the chain resolution of the trigger once it's on the chain — Thrill of the Hunt's [Reaction] is what lets you act in that closed state. One distinction worth noting: just moving the unit (e.g., to Base) would not invalidate the target, since Rex's trigger has no location restriction (FAQ #9612) — you need the unit to leave the board, which is exactly what Thrill of the Hunt does.