You can unlink a Child Global trouble ticket from its Parent trouble ticket from the Edit Global Trouble Ticket window:
To unlink a Child Global trouble ticket from its Parent trouble ticket:
From either the Global Trouble Tickets or the trouble ticket Search Results window, right-click on the desired Child Global trouble ticket and select View (if Child trouble ticket is closed) or Edit (if Child trouble ticket is open).
Click the Actions button in the bottom left-hand corner of the window, and select Unlink Parent Trouble.

The Child Global trouble ticket is unlinked from its Parent trouble ticket and converted back to a basic Global trouble ticket (not a Child or a Parent). The Parent Trouble field is cleared in the Edit Global Trouble Ticket window.
Click Save to close the Edit Global Trouble Ticket window and remove the Child status from the Global trouble ticket.