Trials is elimination mode, but there are separate grimoire cards for them. Trials of Osiris has a card, and the Elimination mode itself has a card that only unlocks when you play the non-trials version of that mode. Elimination has been available one week so far. The Elimination card has tiers for round wins (like rumble, skirmish, control, clash, and salvage have tiers for match wins). Round wins in Trials of Osiris count for these, but the card itself doesn't unlock from Trials.