Updated Answer:
Add the following code in a custom plugin.
function modify_orders_after_query($request) {
$request['date_query'][0]['column'] = 'post_modified';
return $request;
}
add_filter( "woocommerce_rest_shop_order_query", 'modify_orders_after_query' );
Then you can make GET request to your API url, Something like this:
http://example.com/wp-json/wc/v1/orders?after=2016-10-10T10:10:10Z
Notice: Please test before using this method.
Legacy:
This can be achieved with updated_at_min
.
Please check wp-content\plugins\woocommerce\includes\api\class-wc-api-resource.php
: Line 157
and wp-content\plugins\woocommerce\includes\api\class-wc-api-orders.php
: Line 723