By default Green does not collect any Personal Identifiable Information (PII).
Optionally, and only if you create a multisig 2FA protected account, Green will give you the option to enable two factor authentication. If you choose to receive your 2FA via Email, or Telephone number this will be the only Personal Identifiable Information (PII) collected by Blockstream to enable the 2FA security service.
At any moment you can ask us to get your PII deleted:
1.
Make sure your 2FA protected account is empty
2.
Open Settings -> Recovery -> Delete Wallet