Is it permissible for the Ministry of Hajj to add 20% to the amount deposited by the pilgrim, in return for holding the money, treating it like a bank transaction?

Depositing money for a percentage increase is precisely usury (riba), and it requires repentance and returning the increment while keeping the principal. The Hajj of one who did not return the increment is valid according to the majority of scholars, but it is accompanied by sin and a reduction in reward.