This CSS style applies to links inside a table which the class property is not set,
.gridpager a:link, a:active, a:visited, a:hover
{
color: #77A22E;
}

I need to set color of child links only which are inside the sections which the class property is gridpager
What am I missing here?
You need the
.gridpagerselector on each item in your list:(Each item in the list is an independent selector—you have to start from scratch after each comma.)