Despite not having completing this quest before, Eitrigg doesn't appear to be giving this quest to everyone.
Given the line 'he will grow to see your people as a valuable ally' I imagine it is possible that this is either a Goblin Only or Tauren Only quest line as both Orcs and Trolls pass through Razor Hill before they visit Orgrimmar for the first time.
Quest
Return to Eitrigg
A World of Warcraft quest in Orgrimmar. Facts and objectives from the current retail game data.
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Quest facts
The client quest POI data records no map location for this quest, so no map is shown.
Check whether you have already completed this quest
in-game: /run print(C_QuestLog.IsQuestFlaggedCompleted(26807))
Requirements
Read from the Blizzard quest API.
Description
Since you've already spoken to Doras, you'll be able to hire a wind rider to take you right back to Orgrimmar. Each time you arrive in a new town, be sure to speak with the town's flight master. After that, you'll be able to use the flight master's services to travel quickly. Speak to me again when you're ready to purchase a return flight to Orgrimmar. Bring those reports to Eitrigg in the Valley of Strength once you've landed.
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Reward details
Reputation: Orgrimmar +150
Founded by Thrall, this Horde capital city is home to many of the proud orc clans of Durotar.
Reputation group: Horde.
Other quests in Orgrimmar that reward Orgrimmar reputation: Victory for the Horde (+500), For All To See (+500), The Lord of Blackrock (+500), Meeting the Orcs (+250), A Most Puzzling Circumstance (+500), Message for Saurfang (+350).
Item facts are the current retail client’s (ItemSparse); the specialisations for a pick-one item are the ones the Blizzard quest API lists; faction and currency text is the client’s own. Lowest listed price = the US commodity auction house now.