It kind of depends on what database you are linking to and whether or not it
is password protected.  However you can minimize and/or eliminate the
password prompt by checking a box labeled "Save Password" when you establish
your ODBC link.  I haven’t used this with MS Access 2003 however it works for
all versions earlier than 2003.  

If you have already established your link and it’s prompting you for a
password, then you need to remove the link and reestablish it, checking the
save password box. Also if you are linked to an Oracle DB you may find that
you have to enter a password the first time you access the DB.  Oracle
doesn’t have a User Id and password in the Window's ODBC driver set up and
therefore it requires you to enter a User Id and password when you initially
establish the link.

Hope this helps!

When you link the table, tick the "Save Password" box