We don't find this incident in Valmiki Ramayanam.
But this story is found in the Skanda Purana. So maybe this story belongs to some other kalpa.
When ShriRama slayed Ravana, his brother Vibhishana requested him to destroy the bridge.
- With the palms joined in reverence, Vibhīṣaṇa who was conversant with Dharma, requested the noble-souled Rāghava, the slayer of Rāvaṇa
who was staying there:
74-75a. “By this Setu of yours, O Rāma, all the kings superior in
power may come to my city and harass me. Hence, O scion of the family
of Raghu, break this Setu with the tip of your bow.”
75b-76. On being requested thus by the descendant of Pulastya,
Rāghava, the delighter of the members of the family of Raghu,
destroyed his own Setu with the tip of his bow. Hence, O Brāhmaṇas,
that Tīrtha became well-known thereafter as Dhanuṣkoṭi.
The place where this incident took place came to be known as Dhanushkoti and it is a very holy pilgrimage.
Source used: Skanda Purana - Brahma Khanda - Setu mahatmya - Chapter 30