As far as I know it’s not possible to query the links directly, but there is definetly a link_updated field in the wp_links table, so you can use wpdb to interact with it and return the latest (modified) links.
There’s also a solution here.
EDIT : Updating a link doesn’t change link_updated, but here is a plugin that can solve that : Link Updated Plugin
Auttomatically update the link_updated field when adding or editing a
link, so you can use Links as a linklist.
EDIT 2 : If using the Links/Bookmarks functionality is too much of a hassle, as it seems it’s really not as flexible as posts, you could also create a custom post type or a post format for Bookmarks and work with that.