In WooCommerce the rest api is used to get data from orders , products , customers..
but how you can customize or add add other api route  to get (fields and value) , ok it's exist many techniques 
first work directly on the core for example inside

WooCommerce connector ready for OroCRM 1.10 , and the big feature is WooCommerce OroCRM Failure cart follow up email (on try to exit tab or browser) , persist cart and create abandoned cart.

Establish bi-directional connection between  (Open source CRM ) OroCRM and WooCommerce ,you can import customer order coupons and abandoned cart to CRM , for centralize the management of sales marketing and reporting , OroCRM, it can be used for anything related to your store marketing, sales, and customer services ,The WooCommerce Connector allows merchants to get a 360° view of every customer , recover abandoned cart and recover order

Ibnab almost finish a nice connector for OroCRM and WooCommerce , you can import customer order coupons and abandoned cart to crm , for centralize the work on sales and marketing