Grenzo's Cutthroat

The +1/+1 counter is put on the creature before blockers are declared.

In a Two-Headed Giant game, dethrone will trigger if the creature attacks either player on the team with the most life or tied for the most life.

Once dethrone triggers, it doesn't matter what happens to the players' life totals before the ability resolves. You'll put a +1/+1 counter on the creature even if the defending player doesn't have the most life as the ability resolves.