Why does github show me "Your recently pushed branches"?

What I did to remove those messages was to actually create the pull request and then after that, I labeled the pull request as closed. It didn't affect my repository in any sort of way and it did remove the message.

In my situation this message disappeared themself after about 2 hours.

Those links let you quickly compare or open a pull request from one your branch. They're displayed when a recently pushed branch is ahead of the remote HEAD. Most of the time, the remote HEAD points to master (this can be changed by tweaking the "default branch" of the repository in the Admin section).

As it looks like your remote HEAD points to master, those links should not be displayed indeed. The good move would be to send a mail [email protected]..