How to decline a guest

I don't think there's a nice way to do this. I would just keep these people as guests. Actions have consequences, and consider this a lesson learned.

You shouldn't have posted publicly on social media, because then anyone can respond. You should delete the post & make a list of people who you want to invite not who responds to your post. Also, if you're really only concerned about close family/friends who want to come, then shoot them a text or DM.

I agree with the others. Putting things on social media opens up the floodgates so be mindful of that in the future. I agree to delete the post and personally message those people saying how the post was intended but that we have to keep the guest list small so that you won't be able to extend and invitation and it was a faux pas on your end. You would be surprised how people you barely speak to or did not attend their wedding will want to come to your wedding. I would only send invites to those you want to attend not through a post. Even if you want to be cost effective and do an e-vite you should still send a formal invitation to people that you want to attend instead of a post. Not trying to sound harsh but for this kind of event an official invitation should be given, even if electronically.

I agree with the PPs, you should never post anything like that on social media, it would be best t reach out to those individuals on private message if social media is the only way to get ahold of them.

You can not invite them, but if that is what you decide, you should reach out and explain why. It would be considered rude now to disinvite them, since you technically did with the post. I agree this is a lesson learned!