You need to only modify the added rows. Unfortunately, ImportRow does not return the newly created row, but according to the manual all new rows are added to the end of the datatable, so you can access them by index:
int numberOfRowsToCopy = dataGridView1.SelectedRows.Count;
int numberOfExistingRows = dataGridView2.Rows.Count;
foreach(DataGridViewRow row in dataGridView1.SelectedRows)
{
((DataTable)dataGridView2.DataSource).ImportRow(((DataRowView) row.DataBoundItem).Row);
}
for(int i = 0; i < numberOfRowsToCopy; ++i)
{
dataGridView2.Rows[numberOfExistingRows + i].Cells[2].Value = dtp_Datum.Value.ToString();
}