I checked both seasons and the airdates match the original network, Amazon Prime.

I understand that the prime site gives another date, but I can find several sources saying that it is January 18 for season 3 (and every 7 days). For example the trailer at the end is the 18th https://www.youtube.com/watch?v=-7USlC956z8 or a promotional tweet https://twitter.com/thegrandtour/status/1082281951489417216 https://twitter.com/thegrandtour/status/1081916309229711360

And I'm pretty sure I can find more tweets for Season 1.

I understand that the prime site gives another date, but I can find several sources saying that it is January 18 for season 3 (and every 7 days)

This is a bit confusing but the content usually drops on Amazon at midnight GTM. The release date probably depends on whether we count the series as a British or an American series?