Does Wily Newtfish keep its +1 between turns?

No, Wily Newtfish does not keep the +1 Might bonus between turns.

According to the card's text, the bonus is granted "if you've gained XP this turn." Because this is a conditional static ability, it continuously checks whether the condition (gaining XP) was met within the current turn. Once your turn ends and a new turn begins, the game state resets, and the condition is no longer met, causing the Wily Newtfish to lose the +1 Might bonus.