There should be a 'suppression' feature to block files from showing up in recent activity. Here is an excellent post from answers.microsoft.com describing the issue:
https://answers.microsoft.com/en-us/msoffice/forum/all/how-to-hide-sharepoint-online-activity-in-home/1ab2a702-36bd-4d4c-a5fd-0486dd8a0aba

People may be working on confidential documents, and this activity should be suppressed from showing up in a recent activity listing. Turning off search is an inadequate option, people who have access to a document library need the ability to search it.