Thanks, BeingMaverick. That brings me closer to the solution, I guess. so, "http://twitter.com/share" is not from your plugin?
But it looks identical to your Twitter button in the box below.
I looked at all plugins and I thought it could be Jetpack which I had activated for a while then deactivated. I deleted Jetpack. I emptied the cache. All files are gone but the twitter box is still there.
I have 14 plugins and only yours and "oa-social login" have something to do with Twitter, but "oa-social login" buttons look different and only appear for login.