SEO query after WP site move

Hi,

I followed the instructions for moving my site from a subdirectory to the root (using this page: https://codex.www.ads-software.com/Giving_WordPress_Its_Own_Directory), and everything is working fine, but I still see https://mysite/wordpress/my-page/ when I hover over links. They redirect fine to the root but are there any SEO implications in the /wordpress/ part still being there? Do I need to go through my pages and manually remove /wordpress/ from all the links?

Thanks