She can contact you, but it's your call to decide
if you want to reciprocate her response. Therefore, your confusion
is due to your act of reciprocating.
Sometimes, I find it silly for people to go back to their ex-love
who has betrayed them blatantly. The 'extra-dosage of affection'
poured from her action after you had acrimoniously left her is
probably motivated by guilt and revelation.
You think is spurred from love? I seriously doubt it.
Some people sympathised that it could be a moment of folly; but
loyalty is one thing that cannot be compromised in any context of a
proper, serious relationship. You cannot use loyalty as a
expendable commodity, having to revise the definition of loyalty
according to the flow of circumstances. I think that makes a
relationship pretty much 'unrelationship' and makes the pursuit of
love very intense.
That point alone differentiates a fling from a relationship, in
which I can see some post advocating towards the former, in your
list of possible... available choices.
If you can't handle it, I suggest you avoid putting yourself in
such predicament. If her contact is causing you so much confusion,
then cut them to gain clarity.
Remember: you are responsible for your own emotional well being.

Cheers