Your best bet is to customize the content of those email messages a bit. For the confirmations, go to the settings page and under the Confirmation Emails tab, edit the subject and body of the confirmation email to your taste. Something a little more verbose and less general than the default values here will probably have a better chance of getting past spam filters.
Same idea with the target petition emails... try experimenting with the text content of your subject and message body to see if you have better results.
The criteria that different email systems use to identify spam is a little fuzzy, so there's no sure-fire way to deal with the issue.