This letter is to inform you that the gender information of Rebecca and Thomas is already updated as female and male in our records.
A potential problem with this sentence (and one that I see very frequently working with people from certain countries) is the use of the word already. I assume someone issued a request here to update the gender records, and you completed the request? If that is right, you should not say is already updated, but instead, has been updated.
Is already updated means that it was updated before they even made the request. For example, if there were duplicate requests.
Using already can be taken as very slightly offensive because it can imply "you need not have made this request, we were already handling this issue before you said anything."