The grammatical classification of "Without delay" in the sentence "Our teacher wanted that work to be done without delay" is (C) Adverb phrase.
Adverb phrases modify verbs, adjectives, or other adverbs to provide information about time, place, manner, degree, or condition. In this sentence, "without delay" modifies the verb "done" and provides information about how the work should be done. It specifies that it should be done promptly or without any delay.