Rewards live on the token, not the wallet. When an owner lists without claiming, that ETH goes with the owl. Buy it, claim it, keep it.
How to use this. Every owl below is listed on OpenSea right now and carrying rewards its owner never claimed. Compare the listing price to the reward. Buy it, then claim on the rewards page the moment it lands in your wallet.
Reading active OpenSea listings, then checking what each one is carrying.