It's easy enough to set up a filter in Gmail to forward the PayPal e-mails to yourself, and you can set the filter to mark the e-mails as read in the Gmail account.
If you have not already set up YOUR OWN e-mail address in Gmail for forwarding, when creating the filter you will get an e-mail - something along the lines of "Gmail Forwarding Confirmation - Receive Emails from
xx@xx.xx" sent to your own address.
You have to then submit the confirmation code in the e-mail, for the filter to be enabled.