The original iteration of the feature was released last August but at the time, you had to decide who could reply to the tweet while you’re composing it. Once you have published the tweet, you would no longer be able to change the type of Twitter users that can respond to it.
Despite the new update, the way the feature work remains the same. Accessible via the three-dot menu on the top right part of each tweet, you have three options to choose from: everyone (which is the default setting), only people you follow, or only people you mention in the tweet. Tweets with the latter two settings will have the reply icon greyed out except for those you allow. Based on our observations, this option is not limited to just newer tweets which could be useful to those whose past ramblings on Twitter suddenly blows up again.
That being said though, users that have been restricted from replying to your tweets are still able to view, retweet, quote tweet, share, and like it. So, the Mute or Block option is still there for your consideration if things really get out of hand. (Source: Twitter.)
