how long before you’re not offended to find out it’s been chucked?

If it’s the kid’s decision, personally, 0 seconds. Though, in that case, if it were just to be thrown away* I’d rather take it back and return it or resell it, perhaps even just for symbolic value so that it isn’t wasted.
This is true for everyone. It’s stupid to hoard useless gifts. But then again, I also consider gifts a bad idea all together.

*If the kid says he wants to sell it to someone, exchange it, gift it,… , that’s reasonable.

If it’s the parent’s decision, infinite time, unless it is rightfully** ruled the gift was inappropriate ^(sorry).

**E.g.: “He’s too old to have plushies.” is not reasonable.