When you have a unit with 2 extra might cast on it and then you play Thrill of the Hunt, does that unit still have the 2 extra might when you play it to a battlefield?

No, the unit does not keep the +2 extra Might.

When Thrill of the Hunt banishes the unit and then plays it to a battlefield, the unit leaves the board entirely. Per Rule 705, all buffs and modifiers are removed when a unit leaves play. The unit then enters as a new game object — it's treated as a fresh copy of the card, carrying only its printed base Might (plus any permanent modifiers like gear might bonuses). Any temporary +2 Might from a spell effect is gone for good. (RiftJudge FAQ #9870 and #11336 confirm this.)