When you will want to add Basket chrome extension you will be asked for Two permissions

Read and change all your data

We require this permission to enable keyboard shortcuts and to save webpages you when you try to save a link in your Basket.

We do not access, store, or transmit any data from a web page besides the URL that you have requested.

Read and change your bookmarks

To help you sync your chrome bookmarks we need this permission. Sync helps you to retain all your categories to reduce huge effort of organizing your contents again. Also Basket has option to automatically add any new bookmark you made in Chrome ( you can disable that from Options if you like)

Other than that Basket doesn't access your bookmarks.