Is it legal to overlay Attention Bars on other people's web pages?

This is completely legal!

We overlay your attention bars over other people's sites with iframes.  Obviously, if the site you have chosen does not allow iframes, then we will not be able to do so. The notable site that does not allow iframes is Amazon

For your attention bar to be shown you do have to drive traffic to the clika.pe link that Attention Monkey gives you.  Obviously we cannot actually alter the contents of the page at the original URL as it isn't ours!