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In general, if you only see the additional addresses when you check out and not on your PayPal account Settings, this would mean that the addresses displayed are gift addresses. This type of addresses are added when you make a guest purchase, or if you add an address at checkout without adding it to your PayPal account. As these are not registered account, you won't have an option to delete them. However, you can submit a request to have them removed to our Customer Service.
If you want to contact our Customer Service, you can click ‘Help & Contact’ at the bottom of any PayPal page to see which options are available. You can also contact us on Facebook (www.facebook.com/PayPal) or on Twitter (@AskPayPal).