Does Rengar's legend trigger open a response window before the +1 Might is applied?

Yes. Rengar's ability is a triggered ability that targets at finalization, then offers a response window before it resolves because it is neither a unit nor gear. When it triggers, Rengar's controller chooses which unit gets +1 Might, and only one unit can be chosen. The opponent can wait to see the target before deciding whether to Gust.