In order to update the Stock Level for Variants from Amazon FBA, first go to My Apps from your main navigation bar and search for Amazon FBA. Then, click on Settings > Channel Sync > Manual Product Sync.
There is a distinction on how the Amazon FBA and TradeGecko integration functions in comparison to other integrations. Amazon FBA controls the inventory level for the Stock that is allocated there. When you click on Manual Product Sync, TradeGecko will make a call out to FBA, check what level they have listed, and then create a Stock Adjustment to set the level to what they have listed.