Hello Spiccico, explanation is in the add-on description, and in that page also -> https://github.com/aaFn/Bookmark-search-plus-2/wiki/Permissions-and-Privacy-policy
Firefox does not give access to its favicons database (the little image besides each bookmark), so the add-on has to fetch them one by one from the bookmarked URLs, on its first start and next ones, until they are all fetched.
If you do not want favicon fetching, and so do not want to have the images, simply disable favicon fetching in the add-on options page.
Of course, as soon as bug https://bugzilla.mozilla.org/show_bug.cgi?id=1315616 is corrected, I will modify the add-on to get the favicons from the FF internal DB, and there will be no more fetching.
Note: Chrome does give access to its favicon DB, but not Firefox today.
Meanwhile, once again, turn off the option if you do not want it.
I hope this clarifies, aaFn.