Aww cute birds!

Anywhoo, I've been doing a bit of reading. I can't find anything that says you should prune the flowers. This link may answer your question (read the paragraph right above Harvest Time) Pepper Gardening 101

Here is another link which may be useful as time goes on if you start to see your flowers dropping off. The Growing Edge Community - Indoor pepper flowers drop off...

After reading I think you should keep the flowers on, and when the peppers start to grow, pick them sooner rather then later to get the maximum yield from the plant.