eval() is the function you need to do that, but I'd advise trying one of these things to minimize the use of eval. Hopefully one of them will make sense to you.
Option 1:
If you possibly can, save the function as a function, not as a string, and use it that way later. Where you actually store the function is up to you.
var funcForLater = clickedOnItem;
// later is now
funcForLater(t.parentNode.id);
or
someObject.funcForLater = clickedOnItem;
// later is now
(someObject.funcForLater)(t.parentNode.id);
Option 2:
Even if you have to store the function name as a string, you can minimize complexity by doing
(eval(settings.functionName))(t.parentNode.id);
which lowers the amount of Javascript you have to construct and eval.
Option 3:
Put all of the action functions you might need into an object, and call them dictionary-style using the string.
// global
itemActions = { click: clickedOnItem, rightClick: rightClickedOnItem /* etc */ };
// Later...
var action = "click"; // Or wherever you got the action name
(itemActions[action])(t.parentNode.id);