Raid Report, along with other third party websites, track metrics differently than Bungie. As you currently only have 2 carries according to the API and in-game trackers, you will need to get 8 more to obtain the emblem. The API did not record any of your carries prior to the fix.
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I personally feel that since raid report pulls from their API, the information must be there and was incorrectly fixed. They had to make a similar fix when the VoG carry emblem wasn't unlocking for people who got the 10 in two different seasons. In this case, in game trackers also did not read 10 but people got the emblem.
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The information Raid Report uses and how it is used is not up to Bungie beyond making it available via the API. As is likely the case here Raid Report simply uses a counter that increases whenever it sees a completed raid with someone new. That is not something Bungie has access to and explains why Raid Report was able to keep track of carries despite the in game tracking issues. Again Raid Report, like all other third party tracking sites, are not Bungie and therefore the information they display can't be relied upon for items such as this. Your only option is to carry 8 more people if you want the emblem.