If you want to use pre-Thunderbolt 3 peripherals like the LaCie Rugged Thunderbolt External Hard Drive (USB 3.0) on the HP Spectre 13.3, you need to use a special adapter like the StarTech Thunderbolt 3 to Thunderbolt Adapter.
As soon as you plug the StarTech Thunderbolt 3 to Thunderbolt Adapter into the Thunderbolt 3 port of the HP Spectre 13.3, a message window pops up on the bottom right corner of your screen, telling you to approve the connected Thunderbolt device before use. Note, you will see the Thunderbolt device that is connected to the StarTech Thunderbolt 3 to Thunderbolt Adapter as the device that needs to be approved (and not the adapter itself).
After selecting 'Always Connect" in the Approve Thunderbolt Devices window, you can see the LaCie Rugged Thunderbolt External Hard Drive (USB 3.0) show up in the Attached Thunderbolt Devices window.
In the Windows Device Manager, we can also confirm the LaCie Rugged Thunderbolt External Hard Drive (USB 3.0) enumerates as a SATA AHCI Controller within the PCI Express Root Complex.
Finally, we can also confirm that file transfers are working well.
The StarTech Thunderbolt 3 to Thunderbolt Adapter works well with the HP Spectre 13.3, allowing it to connect to pre-Thunderbolt 3 peripherals like the LaCie Rugged Thunderbolt External Hard Drive (USB 3.0).