If I Thrill of the Hunt a unit with Punch First, does it lose the buff on resummon?

Yes, the unit will lose the buff from Punch First.

According to Rule 705 and as confirmed by RiftJudge FAQ #9870, when a unit leaves the battlefield (in this case, by being banished by Thrill of the Hunt), it leaves play and all buffs and modifiers are removed from it.

When Thrill of the Hunt resolves and you play that unit to a battlefield, it enters as a new game object. Because it is a new object, it does not retain any previous modifiers, including the +5 Might from Punch First.