Welcome to the Community, @pitkrew. I can walk you through clearing old transactions by deleting or voiding each transaction.

Please know that deleting a transaction will remove them completely while voiding a transaction assigns a zero value to the item but retains the transaction details. Here's how: 

Delete Transactions

1. Open QuickBooks, click the Lists in the main menu bar. 
2. Click Chart of Accounts from the drop-down menu. Then, select to open the account that contains the transactions you want to delete. 
3. Scroll to the transaction in the account screen. QuickBooks displays transactions in date order, with the most recent at the top of the screen.
4. Click to select the transaction you want to remove, then click Edit in the main menu. 
5. Click Delete, then OK to confirm that you want to delete the transaction.

You can repeat this procedure for each transaction you want to delete.

Void Transactions

1. Go to the Lists in the main menu. 
2. Select Chart of Accounts.
3. Click to open the account with the transactions you want to void.
4. Select the transaction. Click "Edit" in the main menu and then click Void.
5. Click Save and Close to save the voided transaction.

Repeat this procedure for each transaction you want to void.

Here's an article that can guide you on how to match or add bank transactions in QBDT.

For future reference, read through this article: Reconcile an account in QuickBooks Desktop. It helps you learn about balancing your books by matching your actual bank account statements with QuickBooks. 

Feel free to come by here at any time. I'm always here to guide you more with your banking concerns.