My earlier assertions were that Taringail would not have had the political clout to force Andoran Royals to make Galad a Damodred. Without a Published acknowledgment that Galad and/or Taringail was the legal Hier as part of the marriage agreement with Tigrain there was pretty much zero advantage to Mantear in having Galad as a Damodred.

The Game of Houses is exactly what I'm talking about here. The Damodred line needed the union far more than the Mantear line did. Mantear had one Hier, and an ironclad succession, while Damodred had several candidates other than Taringale ... Moiraine, her sisters, Barthanes, probably Caraline and Laman's surviving brothers all could have inherited if the Aiel War didn't happen. Taringale's marriage and the fact that he moved to Andor sound like a Game to keep a Damodred on the Throne after Laman ... A powerful familial alliance with Mantear would go a long way to keep Damodred in power. Galad as a Damodred could potentially muddy those waters even more and I can't see a sitting Queen allowing her Hier to marry into another house when at the time they were in no danger of losing power.

Regardless of Taringail's status as Hier, Mantear either played a rookie move in the Game (very possible) or there is information we don't have on why Galad ended up a Damodred. It's clear what Taringale's end goals were, but it's very unclear as to why the Mantears would have played along for a foreigner. They lost a potentially powerful member of the last Royal line. Even still, you would think the Mantears would have at least made a play to keep Galad as Hgh Seat given his high profile connections at the time of Modreilien's death.