Thanks giori,
For information, on Joomla, ACL and view levels cannot have different behaviors between FRONT and BACK.
I mean, for the same user account, you cannot allow to delete in back and not in front. It is not possible, and it does make sense at all.
But, tell me Mauricio, can a public user delete items in your component ? It is not possible by default. You should make a mistake.
In the sandbox, you can check all this, changing the virtual user. It is the combo box displaying users.
'Me' = Super Administrator.
For other users, check the tooltip button in its right to know what are the current virtual ACLs. Choose 'Guest', and tell us if your 'delete' button still visible. If it is, means that you changed your ACL default configuration of your component.