The CSSF is the "Comission for Surveillance of the Finance Sector". Paypal LU is a credit insitution, but not a bank.

It falls under the CSSF's jurisdiction:

"PayPal has the status of a Luxembourg credit institution and is under the prudential supervision of the Luxembourg supervisory authority, the Commission de Surveillance du Secteur Financier (the "CSSF"). The registered office of the CSSF is located at L-1150 Luxembourg (Luxembourg)."