Filtering lists using LINQ

I would just use the FindAll method on the List class. i.e.:

List<Person> filteredResults = 
    people.FindAll(p => return !exclusions.Contains(p));

Not sure if the syntax will exactly match your objects, but I think you can see where I'm going with this.

Have a look at the Except method, which you use like this:

var resultingList = 
    listOfOriginalItems.Except(listOfItemsToLeaveOut, equalityComparer)

You'll want to use the overload I've linked to, which lets you specify a custom IEqualityComparer. That way you can specify how items match based on your composite key. (If you've already overridden Equals, though, you shouldn't need the IEqualityComparer.)

Edit: Since it appears you're using two different types of classes, here's another way that might be simpler. Assuming a List<Person> called persons and a List<Exclusion> called exclusions:

var exclusionKeys = 
        exclusions.Select(x => x.compositeKey);
var resultingPersons = 
        persons.Where(x => !exclusionKeys.Contains(x.compositeKey));

In other words: Select from exclusions just the keys, then pick from persons all the Person objects that don't have any of those keys.