There is no "Bank reconciliation" balance, so you'll need to help out here.

There is a Bank Statement Balance, which is the number you take off your bank statement and reconcile to. When a reconciliation is posted, the bank statement balance is recorded and cannot be changed.

There is a Bank Balance, which is the previous bank statement balance plus all the outstanding items.

Reversing a cheque marks it as reconciled (no longer outstanding), so your bank balance changes by the amount of the reversed item. The "As at" date controls the date of the transactions sent to the GL.

Which number are you worrying about changing?