On creating an expense entry, if a memo is automatically added to it, you have probably set a default expense memo for the expense item used in the expense entry. You can prevent this from happening by removing the default memo from the Expense Items screen. In the detail view of the expense item, General tab, clear the Memo field and click Save. The memo won't show up on new expense entries created using this expense item.
For existing expense entries that have these default memos, you can use Batch Update in the Expense Entries screen to remove all of them in one go. Check CORE Help Center for details on that.