Create a GPO by using Group Policy Preferences functionality.

The value is stored in HKCU\SOFTWARE\Microsoft\Windows\CurrentVersion\Explorer\StartPage\Favorites

Create or Edit a GPO and expand "User Configuration\Preferences\Windows Settings\Registry"
Add new value and browse to the HKCU\SOFTWARE\...\Favorites if logged on as user that has configured the pinned program or HKEY_USERS\\... if another logged on user has done the pinning.

As it's a binary value containing all pinned programs, it will overwrite any modifications done by user when applying the policy.

If linking GPO to OU with TS-server computer objects, you also nead to enable loopback processing by using "Computer Configuration\Policies\Administrative Templates\System\Group Policy\User Group Policy loopback processing mode"