As confirmed by Blizzard following player discoveries, there is indeed another Quest Reward available during the Season 2 of Battlegrounds. This one is called Partner in Crime and this one gives you your Companion in a golden version when you complete it.
Unlike other Battleground Quest Rewards, Partner in Crime can only be offered under very specific circumstances. All heroes in the lobby must have a valid Companion option (meaning no heroes that arrive after the Companions have left, such as Sir Denathrius or Queen Azshara), and no one playing Sir Finley or Elise Starseeker. If your salon meets these criteria, then there is a 1% chance that it has Partner in Crime. If so, this Reward will be offered to all players.
Have you ever had this chance?