How do I remove invitations I know I wont accept?

In your dashboard (home screen) you've a section called My invitations that lists the events for which you have invitations. Click on one of those to see them. In the popup window all invitations will be listed with a yellow drop down option menu against each one. Normally this is used to accept a particular invitation. But the last option is "I'm not interested in this invite". If you choose that the invite will be removed from your view.

This is a good way to reduce your view of invites to just those that you'd like to consider taking up. And it allows you to see the wood from the trees as new invites appear.