When I have copied a range of cells in one worksheet, then right-click
on a row with the intention of inserting new rows, not the copied
cells, the right-click row menu shows only "Insert copied cells...".
I can work around this by selecting Insert Rows from the Insert menu
on the toolbar.

But I wonder: is there some way to tell Excel "forget about the
copied cells" before I right-click on the row?

I am using Office Excel 2003.