I don't think there's any clean terminology that does what you want without engendering a lot of rules confusion from the mainstream player.
Trying to create a card that does this reminds me of this passage:
The technology involved in making something properly invisible is so mind-bogglingly complex that 999,999,999 times out of a billion it's simpler just to take the thing away and do without it.
Well, this is for a really bad card idea. If it were for an honest card, then the wording is even less of a concern, since this is simply a poor event to attach a reaction to. I usually play with people I trust, and don't scrutinize every move. Published reaction cards, which react to events triggered during an opponent's turn, are always attached to events which require me to do something, and therefore require my momentary attention. For instance, if an opponent plays an Attack card, I'm going to have to do something anyhow, giving me a chance to react with Moat, Secret Chamber, Horse Traders, or Beggar (or bane). If I suddenly gain something that also requires my attention, and thus I can reveal Trader. If I'm made to discard or trash, then again my attention is drawn to the game, so I can reveal Tunnel or Market Square.
The main exceptions that I see are Attack cards with a non-interactive choice, like Pirate Ship or Minion for money. But probably, if there were a clean way of presenting the rules, Donald would have preferred that you not reveal reactions in those scenarios. The other exception is Fool's Gold, but usually an opponent gaining a Province is a significant enough event that I will notice it.
As for this hypothetical card, it is especially taxing to watch for even nonevents when cards are failed to be gained. I mean, when I trash Copper with Remake or Upgrade, I usually don't even consciously acknowledge that I've failed to gain a $1 card. It is just sort of hard coded into my mental understanding that while they upgrade most cards, that they just freebie trash Copper and Curse, with Poor House being some strange rule bending card.