I'm using SendGrid plugin which allows to create a Newsletter Subscription Form that will send email notification to subscribe to newsletter (https://sendgrid.com/docs/for-developers/sending-email/wordpress-subscription-widget/).
I want that when a new user sign-up they will have an option to subscribe on newsletter through checkbox on Register Page (http://prntscr.com/nmq8h2).
I don't really get what you are asking. But I do have a few things to point you in the right direction.
jQuery
should be in it's own file which is loaded using wp_enqueue_scriptThe SendGrid plugin is not anymore maintained since a while (so it seems really outdated).
Updated: Now to add a checkbox for a news letter subscription in Woocommerce registration form (and on My account > Account details section), you will use the following:
Code goes in functions.php file of your active child theme (or active theme). Tested and works.
1) On WooCommerce Registration form:
2) On My account > Account details (section):