Removing a field or changing order can be done using XML, create a layout file in your local theme like:
app/design/frontend/Vendor/Theme/Magento_Checkout/layout/checkout_index_index.xml
and add one of the following options to a field:
<item name="sortOrder" xsi:type="string">100</item>
<item name="visible" xsi:type="boolean">false</item>
your checkout_index_index.xml
will look like this:
<?xml version="1.0"?>
<page xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="urn:magento:framework:View/Layout/etc/page_configuration.xsd">
<body>
<referenceBlock name="checkout.root">
<arguments>
<argument name="jsLayout" xsi:type="array">
<item name="components" xsi:type="array">
<item name="checkout" xsi:type="array">
<item name="children" xsi:type="array">
<item name="steps" xsi:type="array">
<item name="children" xsi:type="array">
<item name="shipping-step" xsi:type="array">
<item name="children" xsi:type="array">
<item name="shippingAddress" xsi:type="array">
<item name="children" xsi:type="array">
<item name="shipping-address-fieldset" xsi:type="array">
<item name="children" xsi:type="array">
<item name="company" xsi:type="array">
<item name="visible" xsi:type="boolean">false</item>
</item>
</item>
</item>
</item>
</item>
</item>
</item>
</item>
</item>
</item>
</item>
</item>
</argument>
</arguments>
</referenceBlock>
</body>
</page>