My Student has used a Scratchcard to create their own Student Account instead of using Account Details I assigned. Can I transfer the license they used to the correct Student Account?

Whilst it is not directly possible to transfer a License from one Student Account to another, you could effectively transfer the license by simply amending the Student details as required in the Students | Find and Edit section of the LabTutor Server Admin Pages.
For example, if a Student Account was created for John Smith with the details:
Username: jsmith
UserID: jsmith

And John created his own account with a scratchcard, with the details:
Username: john
UserID: smith

You could simply amend John's Account details as required. In this Scenario, you'd need to  first change the details of the account you created (as you can't have duplicate Usernames or UserIDs within LabTutor):
Username: jsmith --> jsmith1
UserID: jsmith --> jsmith1
Then:

Username: john --> jsmith
UserID: smith --> jsmith

This also has the benefit of retaining all the Student's work.