1. First, select any cell that is not part of the copied range.
2. Press the "Esc" key on your keyboard. This will deselect the copied range and remove the "marching ants" border around it.
3. Now, right-click on the row where you want to insert new rows. You should see the usual "Insert" options in the right-click menu, such as "Insert Rows" and "Insert Copied Cells".

By deselecting the copied range before right-clicking, you are telling Excel to forget about the copied cells and treat your right-click as a normal operation. This should work in all versions of Excel, including Excel 2003.