Are the messages coming from an email address or a phone number? There are tools in your MyVerizon account that will allow you to block text messages from the web.
I'm most definitely NOT a VZW employee. If a post answered your question, please mark it as the answer.
I think I experience the same situation. Let me give an example. A friend on AT&T who uses an iPhone sends a group text out to 10 of my friends trying to find out what everyone is doing for the weekend. I happen to be out of town for the weekend and don't want to be involved in the conversation. I would like to opt out of getting everyone's responses. I could block all my friends, but I don't want to do that because when I get back to town I want to hear from them. So my question is, "Is there a leave conversation option or opt out like say facebook messenger has?" Is this the same scenario you are looking to avoid?
I have an app "Go SMS Pro" that does block or rather has a Blacklist that blocks sms and will also let you know when messages have been blocked so your able to view and manage which messages you want without all the incoming notifications.
I know what you mean. I don't have unlimited text like other people do so when I get replies from people who are replying to the group it wastes my texts. I was hoping to find an answer myself.