Though you cannot turn off or remove the date range on top of the invoices, you can control how it appears. If you check the option Show billing through on invoices in Settings > Billing & Invoices > Invoice Settings, the invoice displays the date as Billing Through. The date filters in the Invoices > Invoice Filters and Options screen control the Billing Through date on invoices. So, it depends on the date range you select here. If you un-check this option, the invoice displays the range of billing dates (Billing From/To). However, there is no option to hide both dates.
If you try to create invoices with the As of Last Month date filter in the Invoice Filters and Options dialog to include any unbilled time from previous billing periods, this sets the Billing From date on the invoices to 1/1/1970. This happens because CORE uses a date range of 1/1/1970 (which is a set value) to the last date of the previous month when you use the As of Last Month filter. If you do not want this date to show up on the invoices, you should use a custom date range (Filter By > Custom). This lets you control the From and To dates precisely. Another way of handling this is to select the option Show billing through on invoices and then keep the filter As of Last Month so that the invoices show the last day of the previous month as the Billing Through date.
The BQE Custom Reports Team offers the option to create a custom invoice to meet the specific needs of your business and can be contacted for this. Please email them at email@example.com.