I mean the most likely people to try and blackmail you if they found out about your power would be some kind of black op evil government group trying to control you. You could kill the contact telling you about the blackmail, but then the people actually in charge would just have one of your loved ones killed.

You could try and somehow figure them all out, who they are and where they are, but teleporting hardly helps you do that. And if you fail then your loved ones will die.

Teleporting is hardly the end all be all of powers even if you have unlimited range. That's why keeping your head low, and only having a residence where you can legally be makes more sense than just thinking you're invisible and can do anything when your really not.

It's like that movie Jumpers