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.
Store the function
Store the function as a function, not as a string, and use it as a function 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);
Store function name
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 minimizes the amount of Javascript you have to construct and eval.
Dictionary of handlers
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 actionName = "click"; // Or wherever you got the action name
var actionToDo = itemActions[actionName];
actionToDo(t.parentNode.id);
(Minor note: If instead here you used syntax itemActions[actionName](t.parentNode.id);
then the function would be called as a method of itemActions
.)