Answer: Gerund phrase: telling his mother. Noun use: object of the preposition.
Explanation: a gerund is a verb form which functions as a noun (as a subject, direct object, indirect object, object of a preposition, etc), in English they end in "-ing." In the given sentence we can see an example of a gerund phrase in the words "telling his mother" ("telling" is the gerund and "his mother" is a complement), this gerund phrase is acting as the object of the preposition "without" which is place just before it.