Button action procedures can't have arguments. The best you can do is make the variable global:
// declare variables
string $a = "window";
string $b = "layout";
global string $c = "scrollListBox";
// some window creation commands here that i deleted ...
textScrollList -w 100 -h 100 -append "None" -selectCommand "updateChar" $c;
button -l "Refresh" -w 55 -c "refreshChar";
showWindow;
// procedures
proc refreshChar()
{
global string $c;
textScrollList -e -removeAll $c;
textScrollList -e -append "None" $c;
}