How can I prevent end-user from deleting Enrollment Plan such as Vacation?

We have a couple end-users (on separate occasions) that went into an employee's record and successfully deleted their enrollment and they even clicked through the warning message (because not all users pay attention to messages) which deleted their entire vacation accrual history.

We can input it back in and do an adjustment—that's not the problem—we just want to prevent them from having ability to "delete" only.

How do we remove the "Delete" from their view?

Is there some sort of permission/role that we need to customize for something like this?