Shiptheory itself won't pull commodity data from your products in 3dcart, so, instead, there are some default fields you can use in Shiptheory to set a value for these fields on international orders.
To reach the options for setting these default values, you'll want to be in your 3dcart settings page in Shiptheory. Once on the page, scroll to the bottom and click "Advanced Settings" in the bottom left:
Once on the advanced settings, scroll down slightly further and you will reach the Commodity Data settings:
Data that you enter into these fields will then be applied to any products imported from 3dcart to be sent internationally.
If you have any questions regarding this, or have any issues, please feel free to contact support.