You can remove unwanted activities and reports by marking them inactive.
For Case activities and reports go to Administration -> Program Settings -> Program Activity Types or Program Report types.
For Home activities and reports go to Administration -> Organization Settings -> Home activity types or Home Report types.
Edit the activity or report type, check "Inactive", and save.
Note: Any existing activities or reports based upon this type you mark inactive will be unaffected and remain the case or home file tab.