Can I reverse unpaid statement charges so as to get those charges out of A/R?

Hello there, @Janet32.

Yes, you can write it off and declare it as a bad debt so you can clear the invoice out of your accounts receivable. I'll show you how: 

To create an account for bad debt: 

1. From the Lists menu, select Chart of Accounts.
2. In the Chart of Accounts window, right-click anywhere and choose New.
3. In the Add New Account window, click the Expense radio button then choose Continue.
4. Assign the appropriate account number and in the Account Name field, type Bad Debt.
5. Select Save & Close.

To record the bad debt:

1. From the Customers menu, choose Receive Payments.
2. Select the name of the customer from whom you incurred the bad debt.
3. Leave the amount field at $0.00.
4. Highlight the line item that will not be paid.
5. Select Discount & Credits Button.
6. On the Discount tab, enter the bad debt amount in the Amount of Discount field.
7. In the Discount Account drop-down, choose the bad debt expense account created in Step 1, then click Done.
8. Select Save & Close to record the payment.

Once the process is done, this will zero out the Customer Balance. For detailed steps, click this article: Write off bad debt in QuickBooks Desktop.

I've included some articles that can guide you to have an idea about the accounting method in QuickBooks:

• Resolve AR and AP balances on the cash basis Balance Sheet
• Differentiate Cash and Accrual basis
• Write off customer and vendor balances

Please know the Community has your back. If you need further assistance with QuickBooks, click the Reply button and post a comment. I’ll jump right back in to help. Have a good one. 

There are three ways to write these off.  It's basically the same case as if you'd entered an invoice and somehow it won't be paid.

First, if they're recent and you don't mind changing financials for the period, you can just Void them. Done.

Second, you can create new statement charges - perhaps with a current date - where the Qty is negative for the same item and total amount.  Once that's done, then you can use Receive Payments and it's "Discounts and Credits" feature to apply the new statement charges to the old ones, which will link them together much like an invoice and payment, making both of their open balances 0.00.

Third, you can do basically the same thing as just above, but using a Credit Memo transaction.