Moon Icon do not disturb

iPhone 6. There is a moon icon next to two of my contacts (the same two, all the time; no other contacts have it) every time one of them texts me. I ensured my Do Not Disturb is off (in Settings) and when I click on the "i" next to their name within the text message itself there is no option to turn off "do not disturb" nor any option to turn the thread off of do not disturb (these were options recommended to solve the issue) I even deleted the contacts and added them back in and also restarted my phone to no avail. Anyone know how to get the moon icon removed from text messages? Again, Do Not Disturb is turned off; clicking "i" within text message itself does not show option to turn off Do Not Disturb.