From my child theme, how can I remove a library loaded by the parent theme?
You can add overrides to your child theme's info.yml file, telling Drupal not to load the slick library from the parent theme.

Refer to the "Libraries-override" section of this well documented blog post explaining and demonstrating the many options available in terms of removing/replacing files called by other modules and themes with specific ones in your theme.

For your use case, you probably just want to remove (aka disable) both css and js files for slick.js from the parent theme.  So your "library override" will resemble either:

Case 1: slick is part of a library in the parent theme that includes multiple css and js files for the theme, not just slick

libraries-override:
  parent_theme/parent_theme_library_that_includes_slick:
    css:
      theme:
        path_to_parent_theme_or_vendor_slick_library_folder/slick.css: false
        path_to_parent_theme_or_vendor_slick_library_folder/slick-theme.css: false
    js:
        path_to_parent_theme_or_vendor_slick_library_folder/slick.min.js: false


Case 2: slick is part of a standalone library in the parent theme

libraries-override:
  parent_theme/slick_library_name: false


You won't need to declare a replacement in your libraries-override, since you're using the Slick module itself, and it will load relevant files needed.