In the Shopify Admin's order detail page, you will see a section called "Delivery Instructions" if a customer entered additional information when an order was placed using the "Local Delivery" shipping option:

This section combines the local delivery instructions and the phone number to contact.

In EZ Exporter, you can export the delivery instructions and phone number by selecting the following fields:

fulfillment_orders.delivery_method.additional_information.instructions	Fulfillment Orders Delivery Method Instructions (type: text). The delivery instructions to follow when performing the delivery.
fulfillment_orders.delivery_method.additional_information.phone	Fulfillment Orders Delivery Method Phone (type: text). The phone number to contact when performing the delivery.

Here's a sample output: