I’m not 100% sure what you’re trying to do since you’ve indicated you want to change the text, apply CSS, and/or remove it – all of which are different things.
You can filter this content (to change it) with either wpmem_register_links or wpmem_register_links_args
https://rocketgeek.com/plugins/wp-members/docs/filter-hooks/wpmem_register_links/
https://rocketgeek.com/plugins/wp-members/docs/filter-hooks/wpmem_page_links_args/
If you need a specific ID wrapper to specify styles, you could do that by applying a HTML div tag around the [wpmem_form register] shortcode in the page editor. That would be a simple solution without needing to filter anything (although you could use the wpmem_register_links filter to do it.
Another simple way to customize the content (which in this case is the logged in state of the register form shortcode) is to simply nest the content you want for the logged in user using the shortcode as described in the documentation:
https://rocketgeek.com/plugins/wp-members/docs/shortcodes/form/#register
For example:
[wpmem_form register]Anything in here displays when the user is logged in[/wpmem_form]