TEXT list symbols

Does anyone know what the little partial moon symbol is next to names in the message list? I thought it may have something to do with do not disturb or contacts transferring but I am not finding anything like that in any of those settings.

ty : )

Hey, I just tried something, and it worked. When you swipe on the text instead of delete tap sh. ow alerts. Apparently that is how we snooze them. : )