Here's the link to the warranty checker and from there you can also create an RMA:
https://myapps.taec.toshiba.com/myapps/admin/jsp/webrma/addRequest1NoLogin.jsp
Note that the serial# shown in SMART is not complete as is the case for many other brand sof HDDs.
For example a 2TB Toshiba shows the following Serial Number in SMART:
Device Model: TOSHIBA DT01ACA200
Serial Number: Z2U9JKUAS
Firmware Version: MX4OABB0
But if you enter Z2U9JKUAS into the Warranty Checker, it will say "Not Under Warranty" and to "Call Toshiba". On the physical drive, there is a space after Z2U9JKUAS with a "TZ5". You need to enter it as " Z2U9JKUASTZ5" to check the warranty and to do an RMA.
I still have no idea why there is no formal documentation about this from manufacturers or that their system can't work with the main Serial# from SMART.