Last Christmas, my friend gave me a fake Rilakkuma plushie as x'mas gift. She knows I like this cute bear but she doesn't know how to spot fake. So when she gave it to me, she asked me if it's real as the price she paid was not very high. I told her that it's fake BUT I'm still really happy because it's a gift from her.
IMO, if she didn't ask your if the bag is real or fake, she may not even know if there's any real and fake. She may think its a bag with same logo as your bags, thats why she got it for you. Just tell her how much u appreciate her thought and she doesn't need to buy u anything next time, u know she needs those money so a simple lunch or dinner would be the best gift from her!
For the bag, use it to as a storage bag? That's what I did when I received a fake cherry blossom make up pouch, I used it to keep plasters etc and put it in my drawer