There are many reasons why a Recognition may need to be deleted.
In order to be able to delete a Recognition your security Role must have permission to Team Member Management as well as the permission Team Member Management - Delete Recognition.
To delete a Recognition:
Navigate to the Team Member's Profile (Management > Team Members > choose Team Member from roster) and click on the Team Member's Recognition(s) in the top right corner.
Select the Recognition you want to delete.
Click the red trashcan in the top right corner to delete the Recognition.
Deleting a Recognition removes it from everywhere in Woven (Leader boards, Chats, etc).