Hide "home site" button from news post

The special branding on that label comes because your home site is an organizational news site by default. See: https://docs.microsoft.com/en-us/sharepoint/organization-news-site. You can actually remove the "branding" by running PowerShell to take away that super-power, but I wouldn't recommend it because then you will lose another super-power of org news sites - the ability to "boost" news posts. Instead, I agree with Emily that you should consider re-naming the site to be something more relevant to these "official" news articles like News@Contoso or the name of your intranet or Company News. That little banner is super handy whey you see news in other contexts - like in the app bar or in posts in your feed in the mobile app and virtually every other place your users consume news.