Are unused influence tokens handed back to the store after a win or do they accumulate between rounds?
You keep them, though it doesn't say specifically (never says discard them, or keep them specifically), it is implied. In the FAQ section at the back of the rulebook it says:
Q: How many influence tokens can a player have? A: There is no limitation to the number of influence tokens a player can have. If there are not enough influence tokens, record the number of influence token players have on paper or with other some other game pieces.
You would never even come close to running out of influence tokens if you didn't keep them.