• https://support.mozilla.org/en-US/kb/back-and-restore-information-firefox-profiles
• https://support.mozilla.org/en-US/kb/export-firefox-bookmarks-to-backup-or-transfer

There maybe a option in CCleaner for Firefox you are possibly over looking so that it does not clean your bookmarks. Please check the : https://forum.piriform.com/forum/4-ccleaner-discussion/ This is not a Firefox Issue so do please check out the above forum for help if in need.

Malwarebytes does not do anything with Firefox Bookmarks nor anything else unless there is something found. You would have the ability to restore it also.

Please let us know if this solved your issue or if need further assistance.

It is not a good idea to have 3rd party programs 'clean' Firefox files because the wrong things may get lost.

Also, Firefox has the ability to clean itself if you want.

Type about:preferences#privacy<enter> in the address bar. The button next to History, select Use Custom Settings.

At the bottom of the page, turn on Clear History When Firefox Closes. At the far right, press the Settings button. Turn on whatever you want.