how do i remove selected sites from my google arrow pulldown history?

I you are familiar with the Windsows Registry, you can remove items
from here:
HKEY_CURRENT_USER\Software\Google\NavClient\1.1\History

(Note that I'm using version 1.1, your version may be different)

You can then delete individual history entries. Internet Explorer will
then have to be closed and opened again to take effect.

If you are not familiar with using the Windows Registry Editor, you
may wish to defer to someone who is or seek another path.

The only other way I can think of is to do a bunch of searches until
it pushes the one you want removed off the bottom of the list.

Good Luck!

Also note that you can turn off the history altogether under the
Toolbar Options in the Google menu on the toolbar itself.

go to tools on your tool bar, then internet options, the u can do to
general and delete history