If you're certain it's a fee, only the miner can potentially return it.

It would be a gesture of goodwill as they're not obligated to do this because in many jurisdictions there's no clear law for bitcoin transactions and also many miners aren't even legal entities.

If you post the TX it helps know who mined the transaction and if they got your BTC as a fee. I've seen many cases of pools returning fees though. It's good publicity for them.