In the app, open Privacy and data, then "Delete my data". If you no longer have the app, get a deletion code from the app (Privacy and data > Delete my data > Get a code for the web) and enter it here. Deleting removes your lists for good.
Deleting removes your name, wishlists, shared gifts and claims from our systems straight away. Backup copies are removed automatically within 30 days. Reports about content may be kept for safety and legal reasons, as explained in our privacy policy.