1.
You're super vague about the situation. To summarize, a girl did what she shouldn't have, you've cut contact for a week, now she's texting, you don't know what to do.

That flows into 2.
There isn't much to tell what you should do, since people don't know how you are, what happened, the circumstance, how she is, and what's between you two.

3.
Are you really going to let random people online decide your moral principles?
And by the way not talking to her for a week and then talking to her again is not showing her that you won't deal with stupid non-sense. It's kind of like a child promising his mom he will never talk to her again when she punishes him, but then talks to her when he needs something. If you don't want to deal with her bullshit, then don't talk to her. If you're going to tell her it's through and then let her into your world again, well, that's just a sign of weak character.

Then again as I said, I don't know the situation so do whatever your big juicy heart desires.

Could be a shit test. Its all on you bro. If you want to hit it, then hit it. If not move on. You've got to decide if its a deal breaker.