Suppose you play Harvest in spring. In summer the card 'redeployment' allows you to take it back. Now you play the order card Mobilize. Do you get the supremacy bonus?

My reasoning: No. The rules say: "When resolving an Order card, if it is the current player’s highest numbered card used this year, then he may use the Supremacy Bonus ability on the card in addition to the primary ability." and you have used a card with a higher number (it just isn't on the table anymore).

I would say yes; the rules talk about "played", but they are written with the assumption that once played, they stay down. I don't think they are meant to take the special case of picking orders up into account.

Indeed, it seems like one of the major points behind picking up orders like that is to allow them to not affect supremacy anymore.

I posted this on BGG too, but the answer I got back from Corey is "Only cards on the table count for supremacy."