Is there anyway to get someone out of "attack on sight" mode once diplomacy failed too much?

I am in the first town, most people seem to like me, but this one lady called Teleri Helvi I failed too much on admire/intimidate. She's following me around town, punching me. If I kill her, I go to jail. If I go rest she's waiting outside. What can I do? I thought if someone hits me first I'm allowed to attack back?

You have to wait until she actually hurts you. Since she's punching, that first only downs your stamina - run around a bit and then confront her, wait until you health decreases and then you can finish her. She is an unimportant character, but personally I'd avoid killing anyone unnecessarily...

Of course, there are better solutions - get the spell Calm Humanoids or the Scroll of Tevil's Peace to calm her down. That should give you enough time to talk to her again and bribe her into a more peaceful mood.

Finally, you can also cheat. Open the console, click on Helvi, and type

setfight 0
stopcombat