In WooCommerce version 3.4, the dev team made a change to show the value of free shipping methods (other than actual Free Shipping). This means if you use Local Pickup or other methods of shipping that don’t have a preset or calculated cost, the shipping labels on both the cart and checkout to appear like this: Local Shipping: $0.00
This was an intentional change by WooCommerce. You can read the conversation and reasoning behind it here: https://github.com/woocommerce/woocommerce/pull/18624 and referenced here.
A couple of our customers prefered the old way, where free shipping methods didn’t show a price:
If you too want to hide the zero value price on zero-cost shipping methods, use this filter in your
functions.php file or custom functions plugin: