The answer to your question would be that the sentence that has a misplaced modifier is the following one: Bringing the check to the table, the boys were happy to see the waiter.
A misplaced modifier is a word, phrase or clause that is separated from the word it modifies/describes. Consequently, the sentences sound awkward and even confusing. However, more specifically, the example in question would be a case of a dangling modifier. Dangling modifers are a phrase or clause that is not logically related to the word/words it modifies.
In the example, the sentence does not specify who is bringing the check to the table. Yet, since it is next to "the boys were happy to see the waiter" and because we know what waiters do, the sentence suggests that the waiter is the one bringing the check.
