Galaxy S5 - Blocking (or muting?) Text Messages from Certain Numbers

[AC Question]

My cell phone number must have recently been provided to some solicitation group because over the past couple of months, I have gotten an absolute onslaught of solicitation calls! As soon as I see an unknown number, I silence the ring and immediately add the number to my blocked numbers list so they can never call me again from that particular number. They have now resorted to TEXTING me instead of calling! Ugh! So now I am getting a bunch of junk texts!! I would like to be able to block these solicitation text messages in the same way, but the only thing I can find is "mute conversation." Is that the same thing? What does "mute conversation" do exactly?