I was wondering if a unit that is carrying an objective can just "drop" it and flip it back to it's unclaimed side. I guess you'd do this to like hand it off to another unit and I was wondering if there was any rule restricting this? I thought that it'd just make sense to let them get rid of an objective instead of just having to hold onto it until they go into panic...

There is no “unclaim” action, or anything like that. The only way a token becomes unclaimed is if the leader is defeated or the unit panics.

Once a trooper unit leader uses the card action "Claim" to claim an objective token which it is in base contact with, it must always stay in base contact with that unit leader until as said above... the unit leader is defeated or panicked.

On "Recover the Supplies" card, it says "All Trooper units gain: -> Claim (Claim an objective token that is in base contact with your unit leader.)"

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If were able to drop it, that might be interesting yet not practical. As that most likely would be another card action, then one for another friendly trooper unit. Since there are only 6 rounds, time is the biggest reason why that may never come to exist.

Pretty sure there will never be an "undrop". If there was, I could move, drop next to other unit leader, that could claim and move, etc. Could be abusable.